Weighted norm inequalities in a bounded domain by the sparse domination method
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
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Revista Matemática ComplutenseDate
2021Discipline
MatematiikkaAnalyysin ja dynamiikan tutkimuksen huippuyksikköMathematicsAnalysis and Dynamics Research (Centre of Excellence)Copyright
© The Authors 2020
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
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1139-1138Publication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/35894968
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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).License
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