# A Calderon Zygmund decomposition for multiple frequencies and an application to an extension of a lemma of Bourgain

@article{Nazarov2009ACZ,
title={A Calderon Zygmund decomposition for multiple frequencies and an application to an extension of a lemma of Bourgain},
author={Fedor Nazarov and Richard Oberlin and Christoph Thiele},
journal={arXiv: Classical Analysis and ODEs},
year={2009}
}
• Published 15 December 2009
• Mathematics
• arXiv: Classical Analysis and ODEs
We introduce a Calderon Zygmund decomposition such that the bad function has vanishing integral against a number of pure frequencies. Then we prove a variation norm variant of a maximal inequality for several frequencies due to Bourgain. To obtain the full range of Lp estimates we apply the multi frequency Calderon Zygmund decomposition.
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
Based on the tile discretization elaborated by the author in "The Polynomial Carleson Operator", we develop a Calderon-Zygmund type decomposition of the Carleson operator. As a consequence, through a
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We show a variable coefficient version of Bourgain's multi-frequency lemma. It can be used to obtain major arc estimates for a discrete Stein--Wainger type operator considered by Krause
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We establish a higher dimensional counterpart of Bourgain's pointwise ergodic theorem along an arbitrary integer-valued polynomial mapping. We achieve this by proving variational estimates $V_r$ on
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