Weighted multiparameter local Hardy spaces

Abstract

We apply the discrete multiparameter local Calderón identity and Littlewood–Paley–Stein theory with weights to carry out the weighted multiparameter local Hardy spaces $h_w^p$ of arbitrary $k$ number of parameters $\left(k\ge 3\right)$. We will derive the $\left(h_w^p,h_w^p\right)$ and $\left(h_w^p,L_w^p\right)$ boundedness for multiparameter inhomogeneous singular integral operators with slightly weaker assumptions on the kernel.