Intrinsic square functions on functions spaces including weighted Morrey spaces

Abstract

We prove that the intrinsic square functions including Lusin area integral and Littlewood-Paley $g_{\lambda }^{\ast }$-function as defined by Wilson, are bounded in a class of function spaces include weighted Morrey spaces. The corresponding commutators generated by $BMO$ functions are also considered.

14 pages, we have corrected some mistakes and change the title of the paper. (To appear in BKMS)