Regularity of fractional maximal functions through Fourier multipliers

David Beltran, João Pedro Ramos, Olli Saari

Published 2018-03-07Version 1

We prove endpoint bounds for derivatives of fractional maximal functions with either smooth convolution kernel or lacunary set of radii in dimensions $n \geq 2$. We also show that the spherical fractional maximal function maps $L^{p}$ into a first order Sobolev space in dimensions $n \geq 5$.