Atomic decomposition characterizations of weighted multiparameter Hardy spaces

Abstract

Let w ∈ A_∞. In this paper, we introduce weighted-(p, q) atomic Hardy spaces H_w^p,q(ℤⁿ ×ℤ^m) for 0 < p ⩽ 1, q >q_w and show that the weighted Hardy space H_w^p (ℤⁿ × ℤ^m) defined via Littlewood-Paley square functions coincides with H_w^p,q (ℤⁿ × ℤ^m) for 0 < p ⩽ 1, q > q_w. As applications, we get a general principle on the H_w^p (ℤⁿ × ℤ^m) to L_w^p(ℤⁿ ×ℤ^m) boundedness and a boundedness criterion for two parameter singular integrals on the weighted Hardy spaces.

Keywords

Atomic decomposition / multiparameter Hardy spaces / A_∞ weight

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