各向异性分数次积分算子的加权范数不等式

摘要

Let A be an expansive dilation, α ∈ (0, 1), p := 1/α and function v satisfy the anisotropic Muckenhoupt condition Ap,∞(A). In this paper, we study the boundedness of anisotropic fractional integral operators. By L(p,∞) H?lder's inequality and the σ-subaddictive property of ‖·‖p', 1, we obtain some weighted norm inequalities for anisotropic fractional integral operators associated with the weight vp, which are anisotropic extension of Muckenhoupt and Wheeden [6].%设 A 是一个扩张矩阵, α ∈ [0, 1), p := 1/α 且函数v满足各向异性Muckenhoupt Ap,∞(A)权条件. 本文研究了各向异性分数次积分算子的有界性的问题. 利用L(p,∞) 空间的 H?lder 不等式和范数 ‖·‖p', 1 的 σ-次可加性得到了各向异性分数次积分算子关于权vp的一些加权范数不等式. 这些结果是Muckenhoupt和Wheeden的结果[6]在各向异性情形下的推广.