Weak Gurov-Reshetnyak class in metric measure spaces

2023/05/30 by Myyryläinen, Kim
#42B35 #43A85 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2305.18877

Abstract

We introduce a weak Gurov-Reshetnyak class and discuss its connections to a weak Muckenhoupt A_∞ condition and a weak reverse Hölder 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 Hölder inequality. This comes with an upper bound for the reverse Hölder exponent depending on the Gurov-Reshetnyak parameter which allows the study of the asymptotic behavior of the exponent.

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