JournalsrmiVol. 34 , No. 2pp. 739–766

On the variation of maximal operators of convolution type II

  • Emanuel Carneiro

    Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil
  • Renan Finder

    Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil
  • Mateus Sousa

    Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil
On the variation of maximal operators of convolution type II cover
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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 Rd\mathbb R^d, on the torus Td\mathbb T^d and on the sphere Sd\mathbb S^d. The crucial regularity property that these maximal functions share is that they are subharmonic in the corresponding detachment sets.

Cite this article

Emanuel Carneiro, Renan Finder, Mateus Sousa, On the variation of maximal operators of convolution type II. Rev. Mat. Iberoam. 34 (2018), no. 2 pp. 739–766

DOI 10.4171/RMI/1002