Multilinear Calderón–Zygmund operators on weighted Hardy spaces

Abstract

Grafakos–Kalton [Collect. Math. 52 (2001)] discussed the boundedness of multilinear Calderon–Zygmund operators on the product of Hardy spaces. Then Lerner et al. [Adv. Math. 220 (2009)] defined A~ p weights and built a theory of weights adapted to multilinear Calderon–Zygmund operators. In this paper, we combine the above results and obtain some estimates for multilinear Calderon–Zygmund operators on weighted Hardy spaces and also obtain a weighted multilinear version of an inequality for multilinear fractional integrals, which is related to the classical Trudinger inequality.