Weak gurov-reshetnyak class in metric measure spaces
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY(2024)
Abstract
We introduce a weak Gurov-Reshetnyak class and discuss its connections to a weak Muckenhoupt A infinity condition and a weak reverse Holder 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 Holder inequality. This comes with an upper bound for the reverse Holder exponent depending on the Gurov-Reshetnyak parameter which allows the study of the asymptotic behavior of the exponent.
MoreTranslated text
Key words
Gurov-Reshetnyak class,reverse Holder inequality,doubling measure,metric space
AI Read Science
Must-Reading Tree
Example
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
Generate MRT to find the research sequence of this paper
Chat Paper
Summary is being generated by the instructions you defined