On the variation of maximal operators of convolution type II

Abstract

In this paper we establish that several maximal operators of convolution type, associated to elliptic and parabolic equations, are variation-diminishing. Our study considers maximal operators on the Euclidean space $\mathbb R^d$, on the torus $\mathbb T^d$ and on the sphere $\mathbb S^d$. The crucial regularity property that these maximal functions share is that they are subharmonic in the corresponding detachment sets.