Abstract
In this article, after establishing weighted Plancherel-Pôlya-type inequalities, we introduce a new class of weighted Hardy spaces $H^p_{b,w}$ by using $g$-function, where $w$ is a Muckenhoupt's weight and $b$ is a para-accretive function. Then we show the atomic decomposition and molecular characterization of $H^p_{b,w}$. As applications, we prove the boundedness of Calderón-Zygmund operators between $H^p_{b,w}$ and classical weighted Hardy spaces $H^p_w$.
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