关于各向异性扩张矩阵函数的两个性质

Two Properties of Functions Associated with Anisotropic Dilation

所有特征根的模大于1的n×n实矩阵称为各向异性扩张矩阵.在本文中,作者证明了各向异性BMO函数关于分数次积分交换子的两个等价特征刻画;借助关于扩张矩阵A的阶梯拟范数有级数展开和局部标准正交基,得到了局部L2可积函数的各向异性傅里叶级数展开.

A real n×n matrix A with all its eigenvaluesλsatisfying|λ|>1 is called an anisotropic dilation.In this paper,the authors prove two equivalent characterizations of fractional integral commutators for anisotropic BMO function associated with dilation A;by using the series expansion of step quasi-norm and local orthonormal basis associated with dilation A,we obtain the anisotropic Fourier series expansion of localfunction.