TY - JOUR
T1 - Weighted norm inequalities in a bounded domain by the sparse domination method
AU - Kurki, Emma Karoliina
AU - Vähäkangas, Antti V.
PY - 2020/1/1
Y1 - 2020/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85085354065&partnerID=8YFLogxK
U2 - 10.1007/s13163-020-00358-8
DO - 10.1007/s13163-020-00358-8
M3 - Article
AN - SCOPUS:85085354065
JO - REVISTA MATEMATICA COMPLUTENSE
JF - REVISTA MATEMATICA COMPLUTENSE
SN - 1139-1138
ER -