A two weight inequality for Calderón-Zygmund operators on spaces of homogeneous type with applications Article Swipe
Xuan Thinh Duong
,
Ji Li
,
Eric T. Sawyer
,
Manasa N. Vempati
,
Brett D. Wick
,
Dongyong Yang
·
YOU?
·
· 2020
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2006.05628
YOU?
·
· 2020
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2006.05628
Let $(X,d,μ)$ be a space of homogeneous type in the sense of Coifman and Weiss, i.e. $d$ is a quasi metric on $X$ and $μ$ is a positive measure satisfying the doubling condition. Suppose that $u$ and $v$ are two locally finite positive Borel measures on $(X,d,μ)$. Subject to the pair of weights satisfying a side condition, we characterize the boundedness of a Calderón--Zygmund operator $T$ from $L^{2}(u)$ to $L^{2}(v)$ in terms of the $A_{2}$ condition and two testing conditions. For every cube $B\subset X$, we have the following testing conditions, with $\mathbf{1}_{B}$ taken as the indicator of $B$ \begin{equation*} \Vert T(u\mathbf{1}_{B})\Vert _{L^{2}(B, v)}\leq \mathcal{T}\Vert 1_{B}\Vert _{L^{2}(u)}, \end{equation*} \begin{equation*} \Vert T^{\ast }(v\mathbf{1}_{B})\Vert _{L^{2}(B, u)}\leq \mathcal{T}\Vert 1_{B}\Vert _{L^{2}(v)}. \end{equation*} The proof uses stopping cubes and corona decompositions originating in work of Nazarov, Treil and Volberg, along with the pivotal side condition.
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- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2006.05628
- https://arxiv.org/pdf/2006.05628
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
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https://openalex.org/W3035246167Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2006.05628Digital Object Identifier
- Title
-
A two weight inequality for Calderón-Zygmund operators on spaces of homogeneous type with applicationsWork title
- Type
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preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
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2020Year of publication
- Publication date
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2020-06-10Full publication date if available
- Authors
-
Xuan Thinh Duong, Ji Li, Eric T. Sawyer, Manasa N. Vempati, Brett D. Wick, Dongyong YangList of authors in order
- Landing page
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https://arxiv.org/abs/2006.05628Publisher landing page
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https://arxiv.org/pdf/2006.05628Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2006.05628Direct OA link when available
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Homogeneous, Type (biology), Mathematics, Combinatorics, Space (punctuation), Operator (biology), Measure (data warehouse), Biochemistry, Gene, Computer science, Philosophy, Biology, Transcription factor, Ecology, Chemistry, Repressor, Linguistics, DatabaseTop concepts (fields/topics) attached by OpenAlex
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| abstract_inverted_index.Calderón--Zygmund | 63 |
| abstract_inverted_index.T(u\mathbf{1}_{B})\Vert | 101 |
| abstract_inverted_index.}(v\mathbf{1}_{B})\Vert | 111 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 6 |
| citation_normalized_percentile |