Boundedness of intrinsic square functions on generalized Morrey spaces

Abstract: In this paper, we will study the strong type and weak type estimates of intrinsic square functions including the Lusin area integral, Littlewood-Paley $g$-function and $g^*_\lambda$-function on the generalized Morrey spaces $L^{p,\Phi}$ for $1\le p<\infty$, where $\Phi$ is a growth function on $(0,\infty)$ satisfying the doubling condition. The boundedness of the commutators generated by $BMO(\mathbb R^n)$ functions and intrinsic square functions is also obtained.