Weighted hardy spaces associated to para-accretive functions

In this article, after establishing weighted Plancherel-Pôlya-type inequalities, we introduce a new class of weighted Hardy spaces H_b,w^p 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_b,w^p. As applications, we prove the boundedness of Calderón-Zygmund operators between H_b,w^p and classical weighted Hardy spaces H_w^p.