A1 Journal article (refereed)
Weighted norm inequalities in a bounded domain by the sparse domination method (2021)

Kurki, E.-K., & Vähäkangas, A. V. (2021). Weighted norm inequalities in a bounded domain by the sparse domination method. Revista Matemática Complutense, 34(2), 435-467. https://doi.org/10.1007/s13163-020-00358-8

JYU authors or editors

Publication details

All authors or editors: Kurki, Emma-Karoliina; Vähäkangas, Antti V.

Journal or series: Revista Matemática Complutense

ISSN: 1139-1138

eISSN: 1988-2807

Publication year: 2021

Volume: 34

Issue number: 2

Pages range: 435-467

Publisher: Springer

Publication country: Spain

Publication language: English

DOI: https://doi.org/10.1007/s13163-020-00358-8

Publication open access: Openly available

Publication channel open access: Partially open access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/69810

Publication is parallel published: https://arxiv.org/abs/1910.06839

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

Keywords: partial differential equations; harmonic analysis (mathematics); inequalities (mathematics)

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2021

JUFO rating: 1