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

Emma Karoliina Kurki; Antti V. Vähäkangas

doi:10.1007/s13163-020-00358-8

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

Emma Karoliina Kurki^*, Antti V. Vähäkangas

^*Corresponding author for this work

University of Jyväskylä

Research output: Contribution to journal › Article › Scientific › peer-review

1 Citation (Scopus)

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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 language	English
Pages (from-to)	435–467
Number of pages	33
Journal	Revista Matematica Complutense
Volume	34
Issue number	2
Early online date	1 Jan 2020
DOIs	https://doi.org/10.1007/s13163-020-00358-8
Publication status	Published - May 2021
MoE publication type	A1 Journal article-refereed

Funding

Open access funding provided by Aalto University. Funding was provided by Emil Aaltosen Säätiö (Grant No. 180123 N), Luonnontieteiden ja Tekniikan Tutkimuksen Toimikunta (Grant No. 13308063).

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SCI_Kurki_etal_Revista Matemática Complutense_2021Final published version, 444 KBLicence: CC BY

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

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