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arXiv · 2305.18877

Weak Gurov-Reshetnyak class in metric measure spaces

Kim Myyryläinen
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Abstract

We introduce a weak Gurov-Reshetnyak class and discuss its connections to a weak Muckenhoupt $A_\infty$ condition and a weak reverse H\"older inequality in the setting of metric measure spaces with a doubling measure. A John-Nirenberg type lemma is shown for the weak Gurov-Reshetnyak class which gives a specific decay estimate for the oscillation of a function. It implies that a function in the weak Gurov-Reshetnyak class satisfies the weak reverse H\"older inequality. This comes with an upper bound for the reverse H\"older exponent depending on the Gurov-Reshetnyak parameter which allows the study of the asymptotic behavior of the exponent.

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Kim Myyryläinen. 2023-05-30. Weak Gurov-Reshetnyak class in metric measure spaces. https://arxiv.org/abs/2305.18877

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