Power weight inequalities for spherical maximal functions
arXiv:2602.17613
summary
The paper characterizes the range of exponents for which spherical maximal operators with general dilation sets are bounded on weighted L^p spaces with power weights |x|^α, using the Legendre–Assouad function, and resolves an open problem up to endpoint cases.
Abstract
This paper is about spherical maximal functions with general dilation sets acting on functions in weighted spaces. Aside from endpoint cases, a complete description of the allowable ranges of , is given in terms of the Legendre--Assouad function of the dilation set. This settles, up to endpoints, an open problem of Duoandikoetxea and Seijo.
v2: 18 pages, 1 figure. Added subsection about general weights at the end of the Introduction. Final version to appear
Topics & keywords
#spherical maximal functions#weighted lp spaces#dilation sets#legendre-assouad function#endpoint estimatesspherical maximal operatorweighted inequalitiesLegendre–Assouad functiondilation setsL^p spacesendpoint problem