Weighted norm inequalities in a bounded domain by the sparse domination method

Emma Karoliina Kurki*, Antti V. Vähäkangas

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

We prove a local two-weight Poincaré inequality for cubes using the sparse domination method that has been influential in harmonic analysis. The proof involves a localized version of the Fefferman–Stein inequality for the sharp maximal function. By establishing a local-to-global result in a bounded domain satisfying a Boman chain condition, we show a two-weight p-Poincaré inequality in such domains. As an application we show that certain nonnegative supersolutions of the p-Laplace equation and distance weights are p-admissible in a bounded domain, in the sense that they support versions of the p-Poincaré inequality.

Original languageEnglish
JournalREVISTA MATEMATICA COMPLUTENSE
DOIs
Publication statusE-pub ahead of print - 1 Jan 2020
MoE publication typeA1 Journal article-refereed

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