Regularity of the centered fractional maximal function on radial functions

Abstract

We study regularity properties of the centered fractional maximal function M β . More precisely, we prove that the mapif f is a radial function. For d = 1, the radiality assumption can be removed. This corresponds to the counterparts of known results for the non-centered fractional maximal function. The main new idea consists in relating the centered and non-centered fractional maximal function at the derivative level.