Nikodym sets and maximal functions associated with spheres
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.
Authors
- Alan L. Chang (ORCID: https://orcid.org/0000-0003-1716-0134)
- Jongchon Kim (ORCID: https://orcid.org/0000-0002-0842-8293)
- Georgios Dosidis (ORCID: https://orcid.org/0000-0001-5958-191X)
Institutions
- City University of Hong Kong (HK)
- Washington University in St. Louis (US)
- Charles University (CZ)
Publication Details
- Journal
- Revista Matemática Iberoamericana
- Published
- 2024-12-13
- DOI
- https://doi.org/10.4171/rmi/1519
- Citations
- 2
- Primary Topic
- Advanced Harmonic Analysis Research
- Type
- article
- Field-Weighted Citation Impact
- 1.95
Funders
- Univerzita Karlova v Praze
- City University of Hong Kong
- Deutsche Forschungsgemeinschaft
- Hausdorff Research Institute for Mathematics