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arXiv · 1711.03524

Maximal polynomial modulations of singular integrals

Pavel Zorin-Kranich
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Abstract

Let $K$ be a standard H\"older continuous Calder\'on--Zygmund kernel on $\mathbb{R}^{\mathbf{d}}$ whose truncations define $L^2$ bounded operators. We show that the maximal operator obtained by modulating $K$ by polynomial phases of a fixed degree is bounded on $L^p(\mathbb{R}^{\mathbf{d}})$ for $1 < p < \infty$. This extends Sj\"olin's multidimensional Carleson theorem and Lie's polynomial Carleson theorem.

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BibTeXRIS

Pavel Zorin-Kranich. 2017-11-09. Maximal polynomial modulations of singular integrals. https://doi.org/10.1016/j.aim.2021.107832

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