|
| 摘要: |
| 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Hölder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. |
| 关键词: 各向异性 Muckenhoupt权 分数次积分算子 BMO空间 |
| DOI： |
| 分类号:O174.2 |
| 基金项目:Supported by the National Natural Science Foundation of China (11461065; 11661075) and a Cultivate Project for Young Doctor from Xinjiang Uyghur Autonomous Region (qn2015bs003). |
|
| WEIGHTED NORM INEQUALITIES FOR ANISOTROPIC FRACTIONAL INTEGRAL OPERATORS |
|
SUN Rui-rui,LI Jin-xia,LI Bao-de
|
| Abstract: |
| 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,∞) Hölder'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]. |
| Key words: anisotropic Muckenhoupt weight fractional integral operator BMO space |
