一类多线性广义核奇异积分算子的多重权不等式

Multiple Weight Inequalities for Multilinear Singular Integral Operators with Generalized Kernels

本文建立了一类多线性广义核奇异积分算子在乘积加权Lebesgue空间和乘积加权Morrey空间上的有界性,其中涉及的权为多重权.上述结果推广了具有标准核和Dini型核的多线性Calderón-Zygmund算子的相关结论.此外,在加权Lebesgue空间上获得的有界性结果不需要核的尺寸条件.

In this paper,the boundednesses of multilinear singular integral operators with generalized kernels on product of weighted Lebesgue spaces and product of weighted Morrey spaces are established respectively,where the weight,involved is the multiple weight.The above results generalize the relevant conclusions of the multilinear Calderon-Zygmund operators with standard kernels and Dini kernels.Moreover,the size condition of the kernel function is not required to obtain the boundedness on weighted Lebesgue spaces.