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The John-Nirenberg inequality for Qa (Rn) and related problems

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New John–Nirenberg inequalities for martingales

Statistics & Probability Letters, 2014
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Yi, Rui, Wu, Lian, Jiao, Yong
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The John–Nirenberg Inequality of Weighted BLO Space and Its Applications

The Journal of Geometric Analysis, 2022
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Zhao, Huan, Liu, Zongguang
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Interpolation and the John–Nirenberg inequality on symmetric spaces of noncommutative martingales

Studia Mathematica, 2022
Summary: We prove various John-Nirenberg inequalities on symmetric spaces of noncommutative martingales, including the crude and fine versions, which extend the corresponding results of [\textit{M.~Junge} and \textit{M.~Musat}, Trans. Am. Math. Soc. 359, No.~1, 115--142 (2007; Zbl 1173.46046)] and [\textit{G.-X. Hong} and \textit{T.~Mei}, J.
Bekjan, Turdebek N., Chen, Zeqian, Raikhan, Madi, Sun, Mu   +3 more
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$$H^1$$, BMO, and John–Nirenberg Inequality on LCA Groups

Mediterranean Journal of Mathematics, 2023
Let \(G\) be a locally compact abelian group and let \(\mu\) be an inner regular measure on \(G\) that satisfies \(\mu(K) < \infty\) for every compact subset \(K\) of \(G\). Furthermore, assume that \(G\) has a covering family of sets. Let \(1 < q \leq \infty\), define the atomic Hardy space \(H^{1, q}(G)\) by \[ H^{1,q}(G) = \left\{ \sum_{j =0 ...
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The John-Nirenberg inequality for functions of bounded mean oscillation with bounded negative part

Czechoslovak Mathematical Journal, 2022
In this paper the authors establish the John-Nirenberg inequality suitable for \(b\in BMO\) with \(b^{-}\in L^{\infty}\) where \(b^{-}(x)=-\min\{ b(x),0\}\). As an application the authors give some characterization of the function space of all \(b\in BMO\) with \(b^{-}\in L^{\infty}\) by the weighted boundedness of the commutator with the Hardy ...
Hu, Min, Wang, Dinghuai
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John-Nirenberg inequality for Lipschitz martingale spaces

Mathematical Inequalities & Applications
Summary: In this article, John-Nirenberg inequality for Lipschitz martingale spaces is established.
Ren, Yanbo, Ma, Congbian
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New function spaces of BMO type, the John‐Nirenberg inequality, interpolation, and applications

Communications on Pure and Applied Mathematics, 2005
AbstractIn this paper, we introduce and develop some new function spaces of BMO (bounded mean oscillation) type on spaces of homogeneous type or measurable subsets of spaces of homogeneous type. The new function spaces are defined by variants of maximal functions associated with generalized approximations to the identity, and they generalize the ...
Duong, Xuan Thinh, Yan, Lixin
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John–Nirenberg Type Inequalities for Musielak–Orlicz Campanato Spaces on Spaces of Homogeneous Type

Vietnam Journal of Mathematics, 2019
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Huy, Duong Quoc, Ky, Luong Dang
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Weighted mixed-norm inequality on Doob’s maximal operator and John–Nirenberg inequalities in Banach function spaces

Acta Mathematica Hungarica, 2018
We prove a weighted mixed-norm inequality for the Doob maximal operator on a filtered measure space. We also give some characterizations of martingale BMO spaces in the setting of Banach function spaces. The main method is based on the technique of extrapolation on martingale Banach spaces.
W. Chen, K.-P. Ho, Y. Jiao, D. Zhou
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