Weighted and boundary l p estimates for solutions of the $\partial$ -equation on lineally convex domains of finite type and applications Article Swipe
We obtain sharp weighted estimates for solutions of the equation $\partial$ u = f in a lineally convex domain of finite type. Precisely we obtain estimates in the spaces L p ($\Omega$,$\delta$ $\gamma$), $\delta$ being the distance to the boundary, with two different types of hypothesis on the form f : first, if the data f belongs to L p $\Omega$,$\delta$ $\gamma$ $\Omega$ , $\gamma$ > --1, we have a mixed gain on the index p and the exponent $\gamma$; secondly we obtain a similar estimate when the data f satisfies an apropriate anisotropic L p estimate with weight $\delta$ $\gamma$+1 $\Omega$. Moreover we extend those results to $\gamma$ = --1 and obtain L p ($\partial$ $\Omega$) and BMO($\partial$ $\Omega$) estimates. These results allow us to extend the L p ($\Omega$,$\delta$ $\gamma$)-regularity results for weighted Bergman projection obtained in [CDM14b] for convex domains to more general weights.
Related Topics
Concepts
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- https://arxiv.org/pdf/1704.03762.pdf
- OA Status
- green
- Cited By
- 1
- References
- 8
- Related Works
- 20
- OpenAlex ID
- https://openalex.org/W2951368949
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W2951368949Canonical identifier for this work in OpenAlex
- Title
-
Weighted and boundary l p estimates for solutions of the $\partial$ -equation on lineally convex domains of finite type and applicationsWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2017Year of publication
- Publication date
-
2017-04-12Full publication date if available
- Authors
-
Ph. Charpentier, Yves DupainList of authors in order
- Landing page
-
https://arxiv.org/pdf/1704.03762.pdfPublisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/1704.03762.pdfDirect OA link when available
- Concepts
-
Omega, Convex domain, Boundary (topology), Mathematics, Regular polygon, Type (biology), Exponent, Projection (relational algebra), Domain (mathematical analysis), Combinatorics, Mathematical analysis, Physics, Geometry, Algorithm, Linguistics, Philosophy, Biology, Quantum mechanics, EcologyTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
1Total citation count in OpenAlex
- Citations by year (recent)
-
2018: 1Per-year citation counts (last 5 years)
- References (count)
-
8Number of works referenced by this work
- Related works (count)
-
20Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W2951368949 |
|---|---|
| doi | |
| ids.mag | 2951368949 |
| ids.openalex | https://openalex.org/W2951368949 |
| fwci | |
| type | preprint |
| title | Weighted and boundary l p estimates for solutions of the $\partial$ -equation on lineally convex domains of finite type and applications |
| biblio.issue | |
| biblio.volume | |
| biblio.last_page | |
| biblio.first_page | |
| topics[0].id | https://openalex.org/T10884 |
| topics[0].field.id | https://openalex.org/fields/26 |
| topics[0].field.display_name | Mathematics |
| topics[0].score | 0.9998999834060669 |
| topics[0].domain.id | https://openalex.org/domains/3 |
| topics[0].domain.display_name | Physical Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/2604 |
| topics[0].subfield.display_name | Applied Mathematics |
| topics[0].display_name | Holomorphic and Operator Theory |
| topics[1].id | https://openalex.org/T11049 |
| topics[1].field.id | https://openalex.org/fields/26 |
| topics[1].field.display_name | Mathematics |
| topics[1].score | 0.9991999864578247 |
| topics[1].domain.id | https://openalex.org/domains/3 |
| topics[1].domain.display_name | Physical Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/2604 |
| topics[1].subfield.display_name | Applied Mathematics |
| topics[1].display_name | Advanced Harmonic Analysis Research |
| topics[2].id | https://openalex.org/T12037 |
| topics[2].field.id | https://openalex.org/fields/26 |
| topics[2].field.display_name | Mathematics |
| topics[2].score | 0.9968000054359436 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/2604 |
| topics[2].subfield.display_name | Applied Mathematics |
| topics[2].display_name | Algebraic and Geometric Analysis |
| is_xpac | False |
| apc_list | |
| apc_paid | |
| concepts[0].id | https://openalex.org/C2779557605 |
| concepts[0].level | 2 |
| concepts[0].score | 0.7544311881065369 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q9890 |
| concepts[0].display_name | Omega |
| concepts[1].id | https://openalex.org/C2991999034 |
| concepts[1].level | 3 |
| concepts[1].score | 0.6704736351966858 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q193657 |
| concepts[1].display_name | Convex domain |
| concepts[2].id | https://openalex.org/C62354387 |
| concepts[2].level | 2 |
| concepts[2].score | 0.6390363574028015 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q875399 |
| concepts[2].display_name | Boundary (topology) |
| concepts[3].id | https://openalex.org/C33923547 |
| concepts[3].level | 0 |
| concepts[3].score | 0.6320845484733582 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[3].display_name | Mathematics |
| concepts[4].id | https://openalex.org/C112680207 |
| concepts[4].level | 2 |
| concepts[4].score | 0.6241183876991272 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q714886 |
| concepts[4].display_name | Regular polygon |
| concepts[5].id | https://openalex.org/C2777299769 |
| concepts[5].level | 2 |
| concepts[5].score | 0.6121910214424133 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q3707858 |
| concepts[5].display_name | Type (biology) |
| concepts[6].id | https://openalex.org/C2780388253 |
| concepts[6].level | 2 |
| concepts[6].score | 0.590510368347168 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q5421508 |
| concepts[6].display_name | Exponent |
| concepts[7].id | https://openalex.org/C57493831 |
| concepts[7].level | 2 |
| concepts[7].score | 0.5394540429115295 |
| concepts[7].wikidata | https://www.wikidata.org/wiki/Q3134666 |
| concepts[7].display_name | Projection (relational algebra) |
| concepts[8].id | https://openalex.org/C36503486 |
| concepts[8].level | 2 |
| concepts[8].score | 0.5364336371421814 |
| concepts[8].wikidata | https://www.wikidata.org/wiki/Q11235244 |
| concepts[8].display_name | Domain (mathematical analysis) |
| concepts[9].id | https://openalex.org/C114614502 |
| concepts[9].level | 1 |
| concepts[9].score | 0.5172691941261292 |
| concepts[9].wikidata | https://www.wikidata.org/wiki/Q76592 |
| concepts[9].display_name | Combinatorics |
| concepts[10].id | https://openalex.org/C134306372 |
| concepts[10].level | 1 |
| concepts[10].score | 0.47315487265586853 |
| concepts[10].wikidata | https://www.wikidata.org/wiki/Q7754 |
| concepts[10].display_name | Mathematical analysis |
| concepts[11].id | https://openalex.org/C121332964 |
| concepts[11].level | 0 |
| concepts[11].score | 0.2870432138442993 |
| concepts[11].wikidata | https://www.wikidata.org/wiki/Q413 |
| concepts[11].display_name | Physics |
| concepts[12].id | https://openalex.org/C2524010 |
| concepts[12].level | 1 |
| concepts[12].score | 0.20099255442619324 |
| concepts[12].wikidata | https://www.wikidata.org/wiki/Q8087 |
| concepts[12].display_name | Geometry |
| concepts[13].id | https://openalex.org/C11413529 |
| concepts[13].level | 1 |
| concepts[13].score | 0.06963056325912476 |
| concepts[13].wikidata | https://www.wikidata.org/wiki/Q8366 |
| concepts[13].display_name | Algorithm |
| concepts[14].id | https://openalex.org/C41895202 |
| concepts[14].level | 1 |
| concepts[14].score | 0.0 |
| concepts[14].wikidata | https://www.wikidata.org/wiki/Q8162 |
| concepts[14].display_name | Linguistics |
| concepts[15].id | https://openalex.org/C138885662 |
| concepts[15].level | 0 |
| concepts[15].score | 0.0 |
| concepts[15].wikidata | https://www.wikidata.org/wiki/Q5891 |
| concepts[15].display_name | Philosophy |
| concepts[16].id | https://openalex.org/C86803240 |
| concepts[16].level | 0 |
| concepts[16].score | 0.0 |
| concepts[16].wikidata | https://www.wikidata.org/wiki/Q420 |
| concepts[16].display_name | Biology |
| concepts[17].id | https://openalex.org/C62520636 |
| concepts[17].level | 1 |
| concepts[17].score | 0.0 |
| concepts[17].wikidata | https://www.wikidata.org/wiki/Q944 |
| concepts[17].display_name | Quantum mechanics |
| concepts[18].id | https://openalex.org/C18903297 |
| concepts[18].level | 1 |
| concepts[18].score | 0.0 |
| concepts[18].wikidata | https://www.wikidata.org/wiki/Q7150 |
| concepts[18].display_name | Ecology |
| keywords[0].id | https://openalex.org/keywords/omega |
| keywords[0].score | 0.7544311881065369 |
| keywords[0].display_name | Omega |
| keywords[1].id | https://openalex.org/keywords/convex-domain |
| keywords[1].score | 0.6704736351966858 |
| keywords[1].display_name | Convex domain |
| keywords[2].id | https://openalex.org/keywords/boundary |
| keywords[2].score | 0.6390363574028015 |
| keywords[2].display_name | Boundary (topology) |
| keywords[3].id | https://openalex.org/keywords/mathematics |
| keywords[3].score | 0.6320845484733582 |
| keywords[3].display_name | Mathematics |
| keywords[4].id | https://openalex.org/keywords/regular-polygon |
| keywords[4].score | 0.6241183876991272 |
| keywords[4].display_name | Regular polygon |
| keywords[5].id | https://openalex.org/keywords/type |
| keywords[5].score | 0.6121910214424133 |
| keywords[5].display_name | Type (biology) |
| keywords[6].id | https://openalex.org/keywords/exponent |
| keywords[6].score | 0.590510368347168 |
| keywords[6].display_name | Exponent |
| keywords[7].id | https://openalex.org/keywords/projection |
| keywords[7].score | 0.5394540429115295 |
| keywords[7].display_name | Projection (relational algebra) |
| keywords[8].id | https://openalex.org/keywords/domain |
| keywords[8].score | 0.5364336371421814 |
| keywords[8].display_name | Domain (mathematical analysis) |
| keywords[9].id | https://openalex.org/keywords/combinatorics |
| keywords[9].score | 0.5172691941261292 |
| keywords[9].display_name | Combinatorics |
| keywords[10].id | https://openalex.org/keywords/mathematical-analysis |
| keywords[10].score | 0.47315487265586853 |
| keywords[10].display_name | Mathematical analysis |
| keywords[11].id | https://openalex.org/keywords/physics |
| keywords[11].score | 0.2870432138442993 |
| keywords[11].display_name | Physics |
| keywords[12].id | https://openalex.org/keywords/geometry |
| keywords[12].score | 0.20099255442619324 |
| keywords[12].display_name | Geometry |
| keywords[13].id | https://openalex.org/keywords/algorithm |
| keywords[13].score | 0.06963056325912476 |
| keywords[13].display_name | Algorithm |
| language | en |
| locations[0].id | mag:2951368949 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S4306400194 |
| locations[0].source.issn | |
| locations[0].source.type | repository |
| locations[0].source.is_oa | True |
| locations[0].source.issn_l | |
| locations[0].source.is_core | False |
| locations[0].source.is_in_doaj | False |
| locations[0].source.display_name | arXiv (Cornell University) |
| locations[0].source.host_organization | https://openalex.org/I205783295 |
| locations[0].source.host_organization_name | Cornell University |
| locations[0].source.host_organization_lineage | https://openalex.org/I205783295 |
| locations[0].license | |
| locations[0].pdf_url | |
| locations[0].version | submittedVersion |
| locations[0].raw_type | |
| locations[0].license_id | |
| locations[0].is_accepted | False |
| locations[0].is_published | False |
| locations[0].raw_source_name | arXiv (Cornell University) |
| locations[0].landing_page_url | https://arxiv.org/pdf/1704.03762.pdf |
| authorships[0].author.id | https://openalex.org/A5107860936 |
| authorships[0].author.orcid | |
| authorships[0].author.display_name | Ph. Charpentier |
| authorships[0].affiliations[0].raw_affiliation_string | IMB |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Ph. Charpentier |
| authorships[0].is_corresponding | False |
| authorships[0].raw_affiliation_strings | IMB |
| authorships[1].author.id | https://openalex.org/A5023113086 |
| authorships[1].author.orcid | |
| authorships[1].author.display_name | Yves Dupain |
| authorships[1].affiliations[0].raw_affiliation_string | AUCUN |
| authorships[1].author_position | last |
| authorships[1].raw_author_name | Y Dupain |
| authorships[1].is_corresponding | False |
| authorships[1].raw_affiliation_strings | AUCUN |
| has_content.pdf | False |
| has_content.grobid_xml | False |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://arxiv.org/pdf/1704.03762.pdf |
| open_access.oa_status | green |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-10T00:00:00 |
| display_name | Weighted and boundary l p estimates for solutions of the $\partial$ -equation on lineally convex domains of finite type and applications |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-10-10T17:16:08.811792 |
| primary_topic.id | https://openalex.org/T10884 |
| primary_topic.field.id | https://openalex.org/fields/26 |
| primary_topic.field.display_name | Mathematics |
| primary_topic.score | 0.9998999834060669 |
| primary_topic.domain.id | https://openalex.org/domains/3 |
| primary_topic.domain.display_name | Physical Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/2604 |
| primary_topic.subfield.display_name | Applied Mathematics |
| primary_topic.display_name | Holomorphic and Operator Theory |
| related_works | https://openalex.org/W2950255181, https://openalex.org/W3087815761, https://openalex.org/W2277583493, https://openalex.org/W2957027468, https://openalex.org/W3110972115, https://openalex.org/W2932508224, https://openalex.org/W2556583923, https://openalex.org/W2943075804, https://openalex.org/W2260200029, https://openalex.org/W3026886073, https://openalex.org/W2949159458, https://openalex.org/W2796658427, https://openalex.org/W1529027529, https://openalex.org/W1991420372, https://openalex.org/W3036488474, https://openalex.org/W3099807896, https://openalex.org/W2513630800, https://openalex.org/W3157577275, https://openalex.org/W3100795286, https://openalex.org/W3124329399 |
| cited_by_count | 1 |
| counts_by_year[0].year | 2018 |
| counts_by_year[0].cited_by_count | 1 |
| locations_count | 1 |
| best_oa_location.id | mag:2951368949 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S4306400194 |
| best_oa_location.source.issn | |
| best_oa_location.source.type | repository |
| best_oa_location.source.is_oa | True |
| best_oa_location.source.issn_l | |
| best_oa_location.source.is_core | False |
| best_oa_location.source.is_in_doaj | False |
| best_oa_location.source.display_name | arXiv (Cornell University) |
| best_oa_location.source.host_organization | https://openalex.org/I205783295 |
| best_oa_location.source.host_organization_name | Cornell University |
| best_oa_location.source.host_organization_lineage | https://openalex.org/I205783295 |
| best_oa_location.license | |
| best_oa_location.pdf_url | |
| best_oa_location.version | submittedVersion |
| best_oa_location.raw_type | |
| best_oa_location.license_id | |
| best_oa_location.is_accepted | False |
| best_oa_location.is_published | False |
| best_oa_location.raw_source_name | arXiv (Cornell University) |
| best_oa_location.landing_page_url | https://arxiv.org/pdf/1704.03762.pdf |
| primary_location.id | mag:2951368949 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S4306400194 |
| primary_location.source.issn | |
| primary_location.source.type | repository |
| primary_location.source.is_oa | True |
| primary_location.source.issn_l | |
| primary_location.source.is_core | False |
| primary_location.source.is_in_doaj | False |
| primary_location.source.display_name | arXiv (Cornell University) |
| primary_location.source.host_organization | https://openalex.org/I205783295 |
| primary_location.source.host_organization_name | Cornell University |
| primary_location.source.host_organization_lineage | https://openalex.org/I205783295 |
| primary_location.license | |
| primary_location.pdf_url | |
| primary_location.version | submittedVersion |
| primary_location.raw_type | |
| primary_location.license_id | |
| primary_location.is_accepted | False |
| primary_location.is_published | False |
| primary_location.raw_source_name | arXiv (Cornell University) |
| primary_location.landing_page_url | https://arxiv.org/pdf/1704.03762.pdf |
| publication_date | 2017-04-12 |
| publication_year | 2017 |
| referenced_works | https://openalex.org/W1968014615, https://openalex.org/W1835148113, https://openalex.org/W1972915082, https://openalex.org/W2148540155, https://openalex.org/W2095349732, https://openalex.org/W2042645138, https://openalex.org/W2906855564, https://openalex.org/W2993049485 |
| referenced_works_count | 8 |
| abstract_inverted_index., | 63 |
| abstract_inverted_index.: | 50 |
| abstract_inverted_index.= | 12, 109 |
| abstract_inverted_index.> | 65 |
| abstract_inverted_index.L | 29, 58, 94, 113, 128 |
| abstract_inverted_index.a | 15, 69, 83 |
| abstract_inverted_index.f | 13, 49, 55, 89 |
| abstract_inverted_index.p | 30, 59, 75, 95, 114, 129 |
| abstract_inverted_index.u | 11 |
| abstract_inverted_index.We | 0 |
| abstract_inverted_index.an | 91 |
| abstract_inverted_index.if | 52 |
| abstract_inverted_index.in | 14, 26, 138 |
| abstract_inverted_index.of | 7, 19, 44 |
| abstract_inverted_index.on | 46, 72 |
| abstract_inverted_index.to | 37, 57, 107, 125, 143 |
| abstract_inverted_index.us | 124 |
| abstract_inverted_index.we | 23, 67, 81, 103 |
| abstract_inverted_index.--1 | 110 |
| abstract_inverted_index.and | 76, 111, 117 |
| abstract_inverted_index.for | 5, 133, 140 |
| abstract_inverted_index.the | 8, 27, 35, 38, 47, 53, 73, 77, 87, 127 |
| abstract_inverted_index.two | 41 |
| abstract_inverted_index.--1, | 66 |
| abstract_inverted_index.data | 54, 88 |
| abstract_inverted_index.form | 48 |
| abstract_inverted_index.gain | 71 |
| abstract_inverted_index.have | 68 |
| abstract_inverted_index.more | 144 |
| abstract_inverted_index.when | 86 |
| abstract_inverted_index.with | 40, 97 |
| abstract_inverted_index.These | 121 |
| abstract_inverted_index.allow | 123 |
| abstract_inverted_index.being | 34 |
| abstract_inverted_index.index | 74 |
| abstract_inverted_index.mixed | 70 |
| abstract_inverted_index.sharp | 2 |
| abstract_inverted_index.those | 105 |
| abstract_inverted_index.type. | 21 |
| abstract_inverted_index.types | 43 |
| abstract_inverted_index.convex | 17, 141 |
| abstract_inverted_index.domain | 18 |
| abstract_inverted_index.extend | 104, 126 |
| abstract_inverted_index.finite | 20 |
| abstract_inverted_index.first, | 51 |
| abstract_inverted_index.obtain | 1, 24, 82, 112 |
| abstract_inverted_index.spaces | 28 |
| abstract_inverted_index.weight | 98 |
| abstract_inverted_index.Bergman | 135 |
| abstract_inverted_index.belongs | 56 |
| abstract_inverted_index.domains | 142 |
| abstract_inverted_index.general | 145 |
| abstract_inverted_index.results | 106, 122, 132 |
| abstract_inverted_index.similar | 84 |
| abstract_inverted_index.$\Omega$ | 62 |
| abstract_inverted_index.$\delta$ | 33, 99 |
| abstract_inverted_index.$\gamma$ | 61, 64, 108 |
| abstract_inverted_index.Moreover | 102 |
| abstract_inverted_index.[CDM14b] | 139 |
| abstract_inverted_index.distance | 36 |
| abstract_inverted_index.equation | 9 |
| abstract_inverted_index.estimate | 85, 96 |
| abstract_inverted_index.exponent | 78 |
| abstract_inverted_index.lineally | 16 |
| abstract_inverted_index.obtained | 137 |
| abstract_inverted_index.secondly | 80 |
| abstract_inverted_index.weighted | 3, 134 |
| abstract_inverted_index.weights. | 146 |
| abstract_inverted_index.$\Omega$) | 116, 119 |
| abstract_inverted_index.$\Omega$. | 101 |
| abstract_inverted_index.$\gamma$; | 79 |
| abstract_inverted_index.Precisely | 22 |
| abstract_inverted_index.boundary, | 39 |
| abstract_inverted_index.different | 42 |
| abstract_inverted_index.estimates | 4, 25 |
| abstract_inverted_index.satisfies | 90 |
| abstract_inverted_index.solutions | 6 |
| abstract_inverted_index.$\gamma$), | 32 |
| abstract_inverted_index.$\gamma$+1 | 100 |
| abstract_inverted_index.$\partial$ | 10 |
| abstract_inverted_index.apropriate | 92 |
| abstract_inverted_index.estimates. | 120 |
| abstract_inverted_index.hypothesis | 45 |
| abstract_inverted_index.projection | 136 |
| abstract_inverted_index.($\partial$ | 115 |
| abstract_inverted_index.anisotropic | 93 |
| abstract_inverted_index.BMO($\partial$ | 118 |
| abstract_inverted_index.$\Omega$,$\delta$ | 60 |
| abstract_inverted_index.($\Omega$,$\delta$ | 31, 130 |
| abstract_inverted_index.$\gamma$)-regularity | 131 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 2 |
| citation_normalized_percentile |