Weighted norm inequalities in a bounded domain by the sparse domination method
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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Date
2021-05
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Language
en
Pages
33
435–467
435–467
Series
REVISTA MATEMATICA COMPLUTENSE, Volume 34, issue 2
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.Description
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Citation
Kurki , E K & Vähäkangas , A V 2021 , ' Weighted norm inequalities in a bounded domain by the sparse domination method ' , REVISTA MATEMATICA COMPLUTENSE , vol. 34 , no. 2 , pp. 435–467 . https://doi.org/10.1007/s13163-020-00358-8
