Estimates for Multilinear Commutators of Generalized Fractional Integral Operators on Weighted Morrey Spaces
Estimates for Multilinear Commutators of Generalized Fractional Integral Operators on Weighted Morrey Spaces
复制标题
DOI：
10.1155/2015/670649
复制
发表时间：
2015-04
影响因子：
--
通讯作者：
Sha He;Taotao Zheng;Xiangxing Tao
中科院分区：
文献类型：
--
作者：
Sha He;Taotao Zheng;Xiangxing Tao
设为具有高斯核界的解析半群的无穷小生成元，且为的分数次积分。假设这是一个有限的局部可积函数族，则由和生成的多线性交换子由定义。假设它属于加权BMO空间，得到了加权Morrey空间的有界性。作为特例，当是拉普拉斯算子时，我们还得到了多线性分数次交换子在加权Morrey空间上的有界性。本文的主要结果是对一些已知结果的实质性改进和推广。
Let be the infinitesimal generator of an analytic semigroup on with Gaussian kernel bounds, and let be the fractional integrals of for . Assume that is a finite family of locally integrable functions; then the multilinear commutators generated by and are defined by . Assume that belongs to weighted BMO space, ; the authors obtain the boundedness of on weighted Morrey spaces. As a special case, when is the Laplacian operator, the authors also obtain the boundedness of the multilinear fractional commutator on weighted Morrey spaces. The main results in this paper are substantial improvements and extensions of some known results.