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Endpoint power weight inequalities for spherical maximal functions
Abstract
We prove sharp Lp(|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].
Related
- Endpoint estimates for spherical maximal operators acting on radial functions in hyperbolic spaces
- Strong-type endpoint obstructions for bilinear spherical maximal operators
- The strong type endpoint estimate for the local spherical maximal function
- Sharp power-weight estimates for the fractional spherical maximal operator
- Sharp derivative inequalities for maximal functions
BibTeX
@misc{fraccaroli2026endpoint,
title = {{Endpoint power weight inequalities for spherical maximal functions}},
author = {Marco Fraccaroli and Juyoung Lee and Nikou Lei and Joris Roos and Andreas Seeger},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18316},
eprint = {2610.18316},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18316},
}
RIS
TY - UNPB
TI - Endpoint power weight inequalities for spherical maximal functions
AU - Marco Fraccaroli
AU - Juyoung Lee
AU - Nikou Lei
AU - Joris Roos
AU - Andreas Seeger
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18316
UR - https://arxiv.org/abs/2610.18316
AB - 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].
ER -