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arXiv · 1303.6347

Complex interpolation of couple (X, BMO) for $A_1$-regular lattices

Dmitry Rutsky
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Abstract

Recent results of A. Lerner concerning certain properties of the Fefferman-Stein maximal function are applied to show that $(\BMO, X)_\theta = X^\theta$, $0 < \theta < 1$, for a Banach lattice $X$ of measurable functions on $\mathbb R^n$ satisfying the Fatou property such that $X$ has order continuous norm and the Hardy-Littlewood maximal operator $M$ is bounded in $(X^\alpha)'$ for some $0 < \alpha \leqslant 1$.

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Dmitry Rutsky. 2013-03-25. Complex interpolation of couple (X, BMO) for $A_1$-regular lattices. https://arxiv.org/abs/1303.6347

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