Endpoint mapping properties of spherical maximal operators

Abstract

For a function $f\in L^p({\mathbb{R}}^d)$, $d\ge 2$, let $A_{t}f(x)$ be the mean of $f$ over the sphere of radius $t$ centered at $x$. Given a set $E\subset (0,\infty )$ of dilations we prove endpoint bounds for the maximal operator $M_E$ defined by $M_{E}f(x)={\sup }_{t\in E}|A_{t}f(x)|$.

arXiv comment28 pages

References in corpus (1)

• Singular maximal functions and Radon transforms near L^1

Cited by in corpus (1)

• Spherical maximal functions and fractal dimensions of dilation sets