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Revista Matemática Iberoamericana


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Volume 34, Issue 2, 2018, pp. 739–766
DOI: 10.4171/RMI/1002

Published online: 2018-05-28

On the variation of maximal operators of convolution type II

Emanuel Carneiro[1], Renan Finder[2] and Mateus Sousa[3]

(1) Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil
(2) Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil
(3) Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil

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.

Keywords: Maximal functions, heat flow, Poisson kernel, Sobolev spaces, regularity, subharmonic, bounded variation, variation-diminishing, sphere

Carneiro Emanuel, Finder Renan, Sousa Mateus: On the variation of maximal operators of convolution type II. Rev. Mat. Iberoam. 34 (2018), 739-766. doi: 10.4171/RMI/1002