Intrinsic square functions on the weighted Morrey spaces

Abstract: In this paper, we will study the boundedness properties of intrinsic square functions including the Lusin area integral, Littlewood-Paley $g$-function and $g^*_\lambda$-function on the weighted Morrey spaces $L^{p,\kappa}(w)$ for $1<p<\infty$ and $0<\kappa<1$. The corresponding commutators generated by $BMO(\mathbb R^n)$ functions and intrinsic square functions are also discussed.