各向异性分数次积分算子的加权范数不等式（英文）

WEIGHTED NORM INEQUALITIES FOR ANISOTROPIC FRACTIONAL INTEGRAL OPERATORS

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Holder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.

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¨older＇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].