Two-weight inequality for the heat flow and solvability of Hardy-Hénon parabolic equation

2024/07/25 by Tsutsui, Yohei · 1 citation
#35K15 #42B37 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2407.17704

Abstract

In this article, we provide two-weight inequalities for the heat flow on the whole space by applying the sparse domination. For power weights, such inequalities were given by several authors. Owing to the sparse domination, we can treat general weights in Muckenhoupt classes. As a application, we present the local and global existence results for the Hardy-Hénon parabolic equation, which has a potential belonging to a Muckenhoupt class.

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• Unconditional uniqueness of Hardy--Hénon parabolic equations on Herz spaces

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