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arXiv:1201.1945 [math.CA]AbstractReferencesReviewsResources

Lusin Area Function and Molecular Characterizations of Musielak-Orlicz Hardy Spaces and Their Applications

Shaoxiong Hou, Dachun Yang, Sibei Yang

Published 2012-01-10, updated 2014-01-29Version 4

Lusin Area Function and Molecular Characterizations of Musielak-Orlicz Hardy Spaces and Their ApplicationsLet $\varphi: \mathbb R^n\times [0,\infty)\to[0,\infty)$ be a growth function such that $\varphi(x,\cdot)$ is nondecreasing, $\varphi(x,0)=0$, $\varphi(x,t)>0$ when $t>0$, $\lim_{t\to\infty}\varphi(x,t)=\infty$, and $\varphi(\cdot,t)$ is a Muckenhoupt $A_\infty(\mathbb{R}^n)$ weight uniformly in $t$. In this paper, the authors establish the Lusin area function and the molecular characterizations of the Musielak-Orlicz Hardy space $H_\varphi(\mathbb{R}^n)$ introduced by Luong Dang Ky via the grand maximal function. As an application, the authors obtain the $\varphi$-Carleson measure characterization of the Musielak-Orlicz ${\mathop\mathrm{BMO}}$-type space $\mathop\mathrm{BMO}_{\varphi}(\mathbb{R}^n)$, which was proved to be the dual space of $H_\varphi(\mathbb{R}^n)$ by Luong Dang Ky.

Journal: Commun. Contemp. Math. 15 (2013), no. 6, 1350029, 37 pp
Categories: math.CA, math.FA
Subjects: 42B25, 42B30, 42B35, 46E30
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