Resumen de On the variation of maximal operators of convolution type II

Emanuel Carneiro, Renan Finder, Matheus Souza

• 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 Rd, on the torus Td and on the sphere Sd. The crucial regularity property that these maximal functions share is that they are subharmonic in the corresponding detachment sets.