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

Abstract

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 $L^{1,\kappa }(w)$ for $0<\kappa <1$ and $w\in A_1$, and in the generalized Morrey spaces $L^{1,\Theta }$, where $\Theta$ is a growth function on $(0,+\infty )$ satisfying the doubling condition.

arXiv comment28 pages. arXiv admin note: substantial text overlap with arXiv:1009.6142

Cited by in corpus (1)

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