Boundedness of vector-valued intrinsic square functions in Morrey type spaces

In this paper, we will obtain the strong type and weak type estimates for vector-valued analogues of intrinsic square functions in the weighted Morrey spaces $L^{p,\kappa }(w)$ when $1\le p<\mathrm{\infty }$, $0<\kappa <1$, and in the generalized Morrey spaces $L^{p,\mathrm{\Phi }}$ for $1\le p<\mathrm{\infty }$, where $\mathrm{\Phi }$ is a growth function on $(0,\mathrm{\infty })$ satisfying the doubling condition.