Work

Nikodym sets and maximal functions associated with spheres

Year: 2024

Type: article

Abstract: We study spherical analogues of Nikodym sets and related maximal functions. In particular, we prove sharp L^{p} -estimates for Nikodym maximal functions associated with spheres. As a corollary, any Nikodym set for spheres must have full Hausdorff dimension. In addition, we consider a class of maximal functions which contains the spherical maximal function as a special case. We show that L^{p} -estimates for these maximal functions can be deduced from local smoothing estimates for the wave equation relative to fractal measures.

Source: Revista Matemática Iberoamericana

DOI: 10.4171/rmi/1519

Authors: Alan Chang, Georgios Dosidis, Jongchon Kim

Institutions: Washington University in St. Louis, Charles University, City University of Hong Kong

Language: English

Topic: Advanced Harmonic Analysis Research

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Univerzita Karlova v Praze, City University of Hong Kong, Deutsche Forschungsgemeinschaft, Hausdorff Research Institute for Mathematics

Awards: EXC 2047: Hausdorff Center for Mathematics (HCM), G1600773818, G5256572704