Multilinear integral operators and mean oscillation
نویسندگان
چکیده
Let b ∈ BMO(Rn) and T be the Calderón–Zygmund singular integral operator. The commutator [b,T ] generated by b and T is defined by [b,T ] f (x) = b(x)T f (x)−T (b f )(x). By a classical result of Coifman et al [6], we know that the commutator is bounded on Lp(Rn) for 1 < p < ∞. Chanillo [1] proves a similar result when T is replaced by the fractional integral operators. In [9], the boundedness properties for the commutators from Lebesgue spaces to Orlicz spaces are obtained. As the development of Calderón–Zygmund singular integral operators, fractional integral operators and their commutators (see [7,10,11,15]), multilinear singular integral operators have been well-studied. In this paper, we are going to consider some integral operators and their multilinear operator as follows. Let m be a positive integer and A be a function on Rn. We denote that
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Mean Oscillation and Boundedness of Multilinear Integral Operators with General Kernels
As the development of singular integral operators, their commutators and multilinear operators have been well studied (see [3]–[7], [18]–[20]). Let T be the Calderón-Zygmund singular integral operator and b ∈ BMO(R), a classical result of Coifman, Rochberg and Weiss (see [6]) stated that the commutator [b, T ](f) = T (bf)− bT (f) is bounded on L(R) for 1 < p <∞. The purpose of this paper is to ...
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