Continuity of the gradient of the fractional maximal operator on $W^{1,1}(\mathbb{R}^d)$

Abstract

We establish that the map fand Mα denotes either the centered or non-centered fractional Hardy-Littlewood maximal operator. In particular, we cover the cases d > 1 and α ∈ (0, 1) in full generality, for which results were only known for radial functions.