Hausdorff算子在Herz型空间上的加权估计

Weighted estimates for Hausdorff operators on Herz 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H9lder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.

It was considered the weighted boundeness problem for two kinds of high dimensional Hausdorfl＂ operators on function spaces. First, with HOlder inequality, polar decomposition and so on, the boundness of Hausdofff 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 Hausdofff operator on this space was obtained. The results showed that the high dimensional Hausdofff operators were weighted bounded on the above two types of spaces.