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arXiv · 2501.17651

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

Juha Kinnunen·Juha Lehrbäck·Antti V. Vähäkangas·Dachun Yang
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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 Calder\'on-Zygmund decomposition. In particular, this approach does not rely on reverse H\"older inequalities.

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Juha Kinnunen, Juha Lehrbäck, Antti V. Vähäkangas, Dachun Yang. 2025-01-29. Self-improving properties of weighted norm inequalities on metric measure spaces. https://arxiv.org/abs/2501.17651

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