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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 $b\in BMO(\mathbb R^n)$. We first establish the weighted weak $L\log L$-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 $L^{1,κ}(w)$ for $0<κ<1$ and $w\in A_1$, and in the generalized Morrey spaces $L^{1,Θ}$, where $Θ$ is a growth function on $(0,+\infty)$ satisfying the doubling condition.