Pointwise estimates for rough operators with applications to Sobolev inequalities

2023/07/19 by Hoang, Cong, Moen, Kabe, Pérez, Carlos · 1 citation
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2307.10417

Abstract

We investigate Sobolev inequalities for several rough operators. We prove that several operators satisfy a pointwise bound by the Riesz potential applied to the gradient. From this inequality, we derive several new Sobolev-type inequalities with an operator on the left-hand side.

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