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On the variation of maximal operators of convolution type II
classification
math.AP
keywords
maximalmathbboperatorsconvolutiontypeassociatedconsiderscorresponding
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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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