Boundedness of intrinsic square functions on generalized Morrey spaces

Abstract

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