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Median-Type John–Nirenberg Space in Metric Measure Spaces
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en
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23
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Journal of Geometric Analysis, Volume 32, issue 4, pp. 1-23
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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Funding Information: The author would like to thank Juha Kinnunen and Riikka Korte for valuable discussions. The author would also like to thank the anonymous referee for carefully reading the paper and for constructive comments. The research was supported by the Academy of Finland. Publisher Copyright: © 2022, The Author(s).
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Myyryläinen, K 2022, 'Median-Type John–Nirenberg Space in Metric Measure Spaces', Journal of Geometric Analysis, vol. 32, no. 4, 131, pp. 1-23. https://doi.org/10.1007/s12220-022-00872-9