Hausdorff算子在Herz型空间上的加权估计

摘要

It was considered the weighted boundeness problem for two kinds of high dimensional Hausdorff op -erators on function spaces.First, with H?lder inequality, polar decomposition and so on, the boundness of Hausdorff operators on the homogeneous weighted Morrey-Herz space was established; Then, by the atomic decomposition of the homogeneous weighted Herz-type Hardy space,a sufficient condition for the boundedness of Hausdorff operator on this space was obtained.The results showed that the high dimensional Hausdorff oper-ators were weighted bounded on the above two types of spaces.%研究两类高维Hausdorff算子在函数空间上的加权有界性问题.首先,利用H?lder不等式、极坐标分解等方法,得到两类高维Hausdorff算子在齐次加权Morrey-Herz空间上是有界的;其次,利用齐次加权Herz型Hardy空间上的原子分解理论,得到其中一类高维Hausdorff算子在该空间上有界的充分条件.结果表明:高维Hausdorff算子在两类空间上是加权有界的.