加权耦合型空间上的多线性算子（英文）

Multilinear Operators on Weighted Amalgam-type Spaces

本文证明了,如果满足特定点态估计的多线性算子T和它的多线性交换子、迭代交换子分别在乘积加权Lebesgue空间上有界,那么它们也在加权耦合型空间上有界.作为应用,我们说明了多线性Littlewood-Paley函数、具有卷积或非卷积核的多线性Marcinkiewicz积分和它们的线性交换子和迭代交换子均在乘积加权耦合型空间上有界.引入耦合型Campanato空间后,我们得到了多线性分数次积分算子是从耦合型空间到耦合型Campanato空间上有界的.我们的结果对于线性的分数次积分算子也是新的.

In this paper, we prove that if a multilinear operator T with certain pointwise control condition and its multilinear commutator T∑b and iterated commutator T∏b for b ∈BMO^M are bounded on product weighted Lebesgue spaces, then T, T∑b and T∏b are also bounded on product weighted amalgam spaces. As its applications, we show that multilinear Littlewood-Paley functions and multilinear Marcinkiewicz integral functions with kernels of convolution type and non-convolution type, and their multilinear commutators and iterated commutators are bounded on product weighted amalgam spaces. We also consider multilinear fractional type integral operators and their commutators＇ behaviors on weighted amalgam spaces. In order to deal with the endpoint case, we introduce the amalgam-Campanato spaces and show that fractional integral integral operator are bounded operators from product amalgam spaces to amalgam-Campanato spaces. Our results for the fractional integral operator are also new in the linear cases.