Boundedness of Singular Integrals on Multiparameter Weighted Hardy Spaces

We apply the discrete version of Caldern's identity and Littlewood-Paley-Stein theory with weights to derive the and 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 aaEuro parts per thousand A (1) was needed. Our results in the multiparameter setting can be regarded as a natural extension of boundedness for p > 1 for w aaEuro parts per thousand A (p) to the case of weighted Hardy spaces for p a parts per thousand currency signaEuro parts per thousand 1, but under a weaker assumption that w belongs to the class of product A (aaEuro parts per thousand) weights with respect to rectangles in product spaces.