Self-improving properties of weighted norm inequalities on metric measure spaces

2025/01/29 by Kinnunen, Juha, Lehrbäck, Juha, Vähäkangas, Antti V. +1
#30L99 #42B25 #42B35 #46E30 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2501.17651

Abstract

This work discusses self-improving properties of the Muckenhoupt condition and weighted norm inequalities for the Hardy-Littlewood maximal function on metric measure spaces with a doubling measure. Our main result provides direct proofs of these properties by applying a Whitney covering argument and a technique inspired by the Calderón-Zygmund decomposition. In particular, this approach does not rely on reverse Hölder inequalities.

Related

• The Gehring Lemma in Metric Spaces
• Limiting conditions of Muckenhoupt and reverse Hölder classes on metric measure spaces
• On relations between weak and strong type inequalities for modified\n maximal operators on non-doubling metric measure spaces
• On the extension of Muckenhoupt weights in metric spaces
• Self-improvement of weighted pointwise inequalities on open sets