Singular integrals associated with Zygmund dilations on multiparameter weighted Hardy spaces

The aim of this paper is to establish the boundedness of multiparameter singular integral operators associated with Zygmund dilations on product weighted Hardy spaces in the three-parameter setting. Additionally, we show that this class of operators are bounded on product Hardy spaces associated with ball quasi-Banach function spaces by employing the Rubio de Francia extrapolation technique. The generality of our result is illustrated by their applicability to concrete function spaces such as product Herz spaces and weighted product Morrey spaces. Even in these specific cases, the application yields entirely new results.