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arXiv · 1512.02715

On the variation of maximal operators of convolution type II

Emanuel Carneiro·Renan Finder·Mateus Sousa
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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 $\mathbb{R}^d$, 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.

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Emanuel Carneiro, Renan Finder, Mateus Sousa. 2015-12-09. On the variation of maximal operators of convolution type II. https://doi.org/10.4171/rmi%2F1002

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