On a new type of Inequality related to the Uniform Sublevel Set Problem

2020/05/19 by John Green, Green, John · 1 citation
Mathematics · #26D10 (Primary) #42B99 (Secondary) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:26D10 #msc:42B99

paper · pdf · doi:10.48550/arxiv.2005.09407

25 pages, 0 figures

arxiv created 2020/05/19 · arxiv updated 2020/05/20

Abstract

Recently, Steinerberger proved a uniform inequality for the Laplacian serving as a counterpoint to the standard uniform sublevel set inequality which is known to fail for the Laplacian. In this note, we give an elementary proof of this result which highlights a step allowing for adaptations to other situations, for instance, we show that the inequality also holds for the heat operator. We formulate some naturally arising questions.

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• Lower bounds on L^p quasi-norms and the Uniform Sublevel Set Problem

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