Multi-frequency Calderon-Zygmund analysis and connexion to Bochner-Riesz multipliers
Frederic Bernicot (LMJL)
TL;DR
This paper develops a multi-frequency Calderon-Zygmund analysis framework, establishing unweighted and weighted estimates for these operators and connecting them to Bochner-Riesz multipliers, advancing harmonic analysis techniques.
Contribution
It introduces a general definition of multi-frequency Calderon-Zygmund operators and derives new unweighted and weighted estimates, extending previous work.
Findings
Unweighted estimates for multi-frequency Calderon-Zygmund operators.
Weighted estimates involving a new maximal sharp function.
Connection established between multi-frequency analysis and Bochner-Riesz multipliers.
Abstract
In this work, we describe several results exhibited during a talk at the El Escorial 2012 conference. We aim to pursue the development of a multi-frequency Calderon-Zygmund analysis introduced in [9]. We set a definition of general multi-frequency Calderon-Zygmund operator. Unweighted estimates are obtained using the corresponding multi-frequency decomposition of [9]. Involving a new kind of maximal sharp function, weighted estimates are obtained.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Mathematical Analysis and Transform Methods · Advanced Banach Space Theory