A Note on the Polynomial Carleson Operator in higher dimensions

TL;DR

This paper establishes the boundedness of the Polynomial Carleson operator in higher dimensions for all p between 1 and infinity, extending previous one-dimensional results and adapting existing methods.

Contribution

It proves the L^p-boundedness of the Polynomial Carleson operator in multiple dimensions, generalizing prior one-dimensional and specific higher-dimensional cases.

Findings

Proves L^p-boundedness for 1<p< in higher dimensions.

Extends one-dimensional techniques to higher dimensions.

Builds on previous work by Zorin-Kranich and the author.

Abstract

We prove the $L^p$-boundedness, $1<p<\infty$, of the Polynomial Carleson operator in general dimension. This follows the author's resolution of the one dimensional case as well as the work of Zorin-Kranich on the higher dimensional case in the setting $2\leq p<\infty$. The techniques used in this paper are direct adaptations and natural extensions to the higher dimensional case of the one-dimensional methods developed by the author.