Endpoint estimates for commutators of intrinsic square functions in the Morrey type spaces

In this paper, the boundedness properties of commutators generated by $b$ and intrinsic square functions in the endpoint case are discussed, where $b\in BMO(\mathbb R^n)$\mathrm{.}Wefirstestablishtheweightedweak$L\log L$-type estimates for these commutator operators. Furthermore, we will prove endpoint estimates of commutators generated by $BMO({\mathbb{R}}^n)$functions and intrinsic square functions in the weighted Morrey spaces $L^{1,\kappa }(w)$ for $0<\kappa <1$ and $w\in A_1$, and in the generalized Morrey spaces $L^{1,\mathrm{\Theta }}$, where $\mathrm{\Theta }$ is a growth function on $(0,+\mathrm{\infty })$ satisfying the doubling condition.