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.
Original language | English |
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Article number | 131 |
Pages (from-to) | 1-23 |
Number of pages | 23 |
Journal | Journal of Geometric Analysis |
Volume | 32 |
Issue number | 4 |
DOIs | |
Publication status | Published - Apr 2022 |
MoE publication type | A1 Journal article-refereed |
Keywords
- Doubling measure
- John–Nirenberg inequality
- John–Nirenberg space
- Median
- Metric space
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Median-Type John–Nirenberg Space in Metric Measure Spaces
03/03/2022
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