Median-type John-Nirenberg space in metric measure spaces release_mced4aqgdnheleuxiqetqupeci

by Kim Myyryläinen

Released as a article .

2021  

Abstract

We study the so-called John-Nirenberg space that is a generalization of functions of bounded mean oscillation in the setting of metric measure spaces with a doubling measure. Our main results are local and global John-Nirenberg inequalities, which give weak type estimates for the oscillation of a function. We consider medians instead of integral averages throughout, and thus functions are not a priori assumed to be locally integrable. Our arguments are based on a Calderón-Zygmund decomposition and a good-λ inequality for medians. A John-Nirenberg inequality up to the boundary is proven by using chaining arguments. As a consequence, the integral-type and the median-type John-Nirenberg spaces coincide under a Boman-type chaining assumption.
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Type  article
Stage   submitted
Date   2021-04-12
Version   v1
Language   en ?
arXiv  2104.05380v1
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