6533b7dafe1ef96bd126f67c

RESEARCH PRODUCT

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

Antti V. VähäkangasEmma-karoliina Kurki

subject

Discrete mathematicsosittaisdifferentiaaliyhtälötInequalityGeneral Mathematicsmedia_common.quotation_subject010102 general mathematicsPoincaré inequalityharmoninen analyysi01 natural sciences35A23 (Primary) 42B25 42B37 (Secondary)Harmonic analysis010104 statistics & probabilitysymbols.namesakeMathematics - Analysis of PDEsNorm (mathematics)Bounded functionFOS: MathematicssymbolsMaximal function0101 mathematicsepäyhtälötAnalysis of PDEs (math.AP)Mathematicsmedia_common

description

AbstractWe 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.

yearjournalcountryeditionlanguage
2019-10-15
http://urn.fi/URN:NBN:fi:jyu-202006094053