TY - JOUR
T1 - Hardy-Littlewood maximal operator on the associate space of a Banach function space
AU - Karlovich, Alexei Yu
N1 - info:eu-repo/grantAgreement/FCT/5876/147204/PT
This work was partially supported by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through the project UID/MAT/00297/2013 (Centro de Matemática e Aplicações).
PY - 2019/1/1
Y1 - 2019/1/1
N2 - Let ε(X, d, μ) be a Banach function space over a space of homogeneous type (X, d, μ). We show that if the Hardy-Littlewood maximal operator M is bounded on the space ε(X, d, μ), then its boundedness on the associate space ε'(X, d, μ) is equivalent to a certain condition A∞. This result extends a theorem by Andrei Lerner from the Euclidean setting of ℝn to the setting of spaces of homogeneous type.
AB - Let ε(X, d, μ) be a Banach function space over a space of homogeneous type (X, d, μ). We show that if the Hardy-Littlewood maximal operator M is bounded on the space ε(X, d, μ), then its boundedness on the associate space ε'(X, d, μ) is equivalent to a certain condition A∞. This result extends a theorem by Andrei Lerner from the Euclidean setting of ℝn to the setting of spaces of homogeneous type.
KW - Associate space
KW - Banach function space
KW - Dyadic cubes
KW - Hardy-Littlewood maximal operator
KW - Space of homogeneous type
UR - http://www.scopus.com/inward/record.url?scp=85066759823&partnerID=8YFLogxK
U2 - 10.14321/realanalexch.44.1.0119
DO - 10.14321/realanalexch.44.1.0119
M3 - Article
AN - SCOPUS:85066759823
SN - 0147-1937
VL - 44
SP - 119
EP - 140
JO - Real Analysis Exchange
JF - Real Analysis Exchange
IS - 1
ER -