Atomic decomposition characterizations of weighted multiparameter Hardy spaces

Abstract

Let w\in A_{\infty }. In this paper, we introduce weighted-(p, q) atomic Hardy spaces H_w^{p,q}({ℝ}^n\times {ℝ}^m) for \mathrm{0}\prec p\le \mathrm{1}, q\succ qw and show that the weighted Hardy space H_w^{p,q}({ℝ}^n\times {ℝ}^m) defined via Littlewood-Paley square functions coincides with H_w^{p,q}({ℝ}^n\times {ℝ}^m) for \mathrm{0}\prec p\le \mathrm{1}, q\succ qw. As applications, we get a general principle on the H_w^{p,q}({ℝ}^n\times {ℝ}^m) to L_w^{p,q}({ℝ}^n\times {ℝ}^m) boundedness and a boundedness criterion for two parameter singular integrals on the weighted Hardy spaces.

Key words： Atomic decomposition; multiparameter Hardy spaces; A_∞ weight

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