Riesz-Schur transforms Article Swipe
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Adrián M. González‐Pérez
,
Javier Parcet
,
Jorge Pérez-Garcìa
,
Éric Ricard
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2411.09324
· OA: W4404450652
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2411.09324
· OA: W4404450652
We investigate nontrigonometric forms of Riesz transforms in the context of Schur multipliers. This refines Grothendieck-Haagerup's endpoint criterion with a new condition for the Schatten p-boundedness of Schur multipliers and strengthens Potapov/Sukochev's solution of Arazy's conjecture. We recover as well dimension-free estimates for trigonometric Riesz transforms. Our discrete approach is much simpler than previous harmonic analysis and probabilistic approaches. As an application, we find a very simple proof of recent criteria for Schur multipliers of Hörmander-Mikhlin and Marcinkiewicz type.
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