Name: The elliptic maximal function
Keywords: Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2025Embargo end date: 01 Jan 2023 English Publisher:Elsevier BVJournal:Journal of Functional Analysis, volume 288, page 110,693 (issn: 0022-1236,

Authors: Lee, Juyoung; Lee, Sanghyuk; Oh, Sewook;

doi: 10.1016/j.jfa.2024.110693 , 10.48550/arxiv.2305.16221

arXiv: http://arxiv.org/abs/2305.16221

The elliptic maximal function

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Abstract

We study the elliptic maximal functions defined by averages over ellipses and rotated ellipses which are multi-parametric variants of the circular maximal function. We prove that those maximal functions are bounded on $L^p$ for some $p\neq \infty$. For this purpose, we obtain some sharp multi-parameter local smoothing estimates.

to appear in Journal of Functional Analysis

Keywords

Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics

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