Weighted Variable Hardy Spaces Associated with Para-Accretive Functions and Boundedness of Calderon-Zygmund Operators

The purpose of this paper is threefold. The first is to present a new atomic decomposition of weighted Hardy spaces H-b,w(p)(Rn) associated with para-accretive functions, where w is a Muckenhoupt's weight, b is a para-accretive function and p < infinity. The second purpose is to show the boundedness of Calderon-Zygmund operators on these spaces for p < infinity. The last purpose is to introduce a new weighted variable Hardy space H (p(center dot))(b,w) (Rn) by using the Littlewood-Paley g functions and weighted variable Plancherel-Polya-type inequalities associated with a para-accretive function, where w is a variable exponent weight. Moreover, we also prove the boundedness for Calderon-Zygmund operators on H (p(center dot))(b,w) (R-n) via extrapolation.