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

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

2012-01-10

arxiv.org/abs/1201.1945v3

Mathematics

Classical Analysis and ODEs

32 pages, Submitted

Scientific paper

Let $\varphi: \mathbb R^n\times [0,\infty)\to[0,\infty)$ be a function such that $\varphi(x,\cdot)$ is an Orlicz function, and $\varphi(\cdot,t)$ is a Muckenhoupt $A_\infty(\mathbb{R}^n)$ weight. 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.

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