Abstract
The authors study anisotropic product Hardy spaces Hwp(A→) associated with a pair A→:=(A1,A2) of expansive dilations and a class of product Muckenhoupt weights A∞(A→) on Rn×Rm. This article is a continuation of their earlier work in Bownik et al. (2010) [8]. The authors establish the Littlewood–Paley g-function characterization and the φ-transform characterization of Hwp(A→), 0<p⩽1. The authors also introduce the weighted anisotropic product Campanato space Lp,w(A→) and establish its φ-transform characterization. As an application, the authors identify the dual space of Hwp(A→) with Lp,w(A→). The results of this article improve the existing results for weighted product Hardy spaces on R×R and are new even in the weighted isotropic setting.
Published Version
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