Weighted Norm Inequalities for the Maximal Operator on Variable Lebesgue Spaces Over Spaces of Homogeneous Type

Given a space of homogeneous type (X,μ,d), we prove strong-type weighted norm inequalities for the Hardy-Littlewood maximal operator over the variable exponent Lebesgue spaces L^\pp. We prove that the variable Muckenhoupt condition $\App$ is necessary and sufficient for the strong type inequality if $\pp$ satisfies log-H\"older continuity conditions and 1 < p_- \leq p₊ < \infty. Our results generalize to spaces of homogeneous type the analogous results in Euclidean space proved in [14].

Grantor dc:publisher

University of Alabama Libraries

Year dc:date.issued

2020

Author dc:creator

• Cummings, Jeremy

Advisor dc:contributor.advisor

• Cruz-Uribe, David

Contributors dc:contributor

• Ferguson, Tim
• Moen, Kabe
• Rodney, Scott

• Harmonic analysis
• Maximal operator
• Variable Lebesgue Spaces
• Weighted estimates

Statement dc:rights

• All rights reserved by the author unless otherwise indicated.

Language dc:language.iso

en_US, English

Dc Identifier Other

http://purl.lib.ua.edu/176881
u0015_0000001_0003675
Cummings_alatus_0004M_14220

OAI identifier oai:identifier

oai:ir.ua.edu:123456789/8380