Lipschitz Estimates for Multilinear Commutator of Littlewood-paley Operator
نویسندگان
چکیده
Let T be the Calderón-Zygmund operator, Coifman, Rochberg and Weiss (see [4]) proves that the commutator [b, T ](f) = bT (f) − T (bf)(where b ∈ BMO(R)) is bounded on L(R) for 1 < p <∞. Chanillo (see [2]) proves a similar result when T is replaced by the fractional operators. In [8, 16], Janson and Paluszynski study these results for the Triebel-Lizorkin spaces and the case b ∈ Lipβ(R), where Lipβ(R) is the homogeneous Lipschitz space. The main purpose of this paper is to discuss the boundedness of multilinear commutator generated by Littlewood-Paley operator and bj on Triebel-Lizorkin space, Hardy space and Herz-Hardy space, where bj ∈ Lipβ(R).
منابع مشابه
Continuity for Multilinear Commutator of Littlewood-paley Operator on Besov Spaces
As the development of the singular integral operators, their commutators have been well studied (see [1, 2, 3, 14]). From [2, 3, 9, 13], we know that the commutators and multilinear operators generated by the singular integral operators and the Lipschitz functions are bounded on the Triebel-Lizorkin and Lebesgue spaces. The purpose of this paper is to introduce the multilinear commutator associ...
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