PreprintarXiv licencearXiv
Sharp Lp estimates for the strong spherical maximal operator
Abstract
We prove that the strong spherical maximal operator in ℝn is bounded on Lp for n≥4 and p>(n+1)/(n−1). This establishes the conjecture of Hickman and Zahl in the remaining dimensions. The main ingredient is a local L2 estimate for the pieces obtained by a dyadic decomposition in the normal variable. After squaring one input coordinate, we reduce this estimate to a TT* argument for diagonal quadratic phases.
Related
- Sharp power-weight estimates for the fractional spherical maximal operator
- Sharp weighted estimates for the multilinear maximal operator
- Sharp Lp--Lq bounds for the strong circular maximal operator
- Strong-type endpoint obstructions for bilinear spherical maximal operators
- Stein's generalized spherical maximal operator
BibTeX
@misc{chen2026sharp,
title = {{Sharp $L^p$ estimates for the strong spherical maximal operator}},
author = {Mingfeng Chen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.32421},
eprint = {2609.32421},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32421},
}
RIS
TY - UNPB
TI - Sharp L^p estimates for the strong spherical maximal operator
AU - Mingfeng Chen
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2609.32421
UR - https://arxiv.org/abs/2609.32421
AB - We prove that the strong spherical maximal operator in ℝ^n is bounded on L^p for n≥4 and p>(n+1)/(n−1). This establishes the conjecture of Hickman and Zahl in the remaining dimensions. The main ingredient is a local L^2 estimate for the pieces obtained by a dyadic decomposition in the normal variable. After squaring one input coordinate, we reduce this estimate to a TT^* argument for diagonal quadratic phases.
ER -