𝐿^{𝑝} bound on the strong spherical maximal function

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 17 Dec 2024Embargo end date: 01 Jan 2023 English Publisher:American Mathematical Society (AMS)Journal:Proceedings of the American Mathematical Society, volume 153, pages 1,155-1,167 (issn: 0002-9939, eissn: 1088-6826,

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

doi: 10.1090/proc/17108 , 10.48550/arxiv.2309.15308

arXiv: 2309.15308

𝐿^{𝑝} bound on the strong spherical maximal function

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Abstract

In this note we show that the strong spherical maximal function in R d \mathbb R^d is bounded on L p L^p if p > 2 ( d + 1 ) / ( d − 1 ) p>2(d+1)/(d-1) for d ≥ 3 d\ge 3 .

Keywords

Maximal functions, Littlewood-Paley theory, spherical maximal function, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Primary 42B25, Secondary 35S30, multi-parametric, Fourier integral operators applied to PDEs

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