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What is Muckenhoupt about?

This document explores the 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. The authors present a novel approach that avoids reverse Hölder inequalities, utilizing a Whitney covering argument and Calderón–Zygmund decomposition techniques. The main result demonstrates that if a weight belongs to a certain Muckenhoupt class, it also belongs to a class with a slightly smaller index,

Author

Tuấn Khải Lê

Language

EN