Boundedness of Singular Integrals on Multiparameter Weighted Hardy Spaces H _w ~p(? ~n×? ~m

摘要

We apply the discrete version of Calderón's identity and Littlewood-Paley-Stein theory with weights to derive the (H _w ~p, H _w ~p) and (H _w ~p, L _w ~p) (0 < p ≤ 1) boundedness for multiparameter singular integral operators. It turns out that even in the one-parameter case, our results substantially improve the known ones in the literature where w ∈ A _1 was needed. Our results in the multiparameter setting can be regarded as a natural extension of L _w ~p boundedness for p > 1 for w ∈ A _p to the case of weighted Hardy spaces H _w ~p for p ≤ 1, but under a weaker assumption that w belongs to the class of product A _∞ weights with respect to rectangles in product spaces.