Work

Endpoint power weight inequalities for spherical maximal functions

Year: 2026

Type: preprint

Abstract: We prove sharp $L^p(|x|^α)$ estimate for spherical maximal functions. We resolve the remaining open problem for the full maximal operator for $α=1-d$ and $p<2$ and prove a more general result involving a local version of Assouad dimension of the underlying dilation set. We also make a case study with endpoint bounds for a model case involving convex sequences in $[1,2]$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.18316

Authors: Fraccaroli, Marco, Lee, Juyoung, Lei, Nikou, Roos, Joris, Seeger, Andreas

Institutions: University of Massachusetts Lowell, University of British Columbia, University of Wisconsin–Madison

Language: English

Topic: Advanced Harmonic Analysis Research

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Award: Averaging operators and related topics in harmonic analysis

OpenAlex ID: W7221789207

Cites: 2

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Related to: 10