Abstract

In this paper, we introduce new generalized Hausdorff operators. They include many famous operators as special cases. We obtain necessary and sufficient conditions for these operators to be bounded on the weighted Herz spaces. The corresponding new operator norm inequalities are obtained. They are significant improvements and generalizations of many known results. Several open problems are formulated.

Keywords: Hausdorff operator; weighted Herz space; norm inequality.

MSC: 26D10, 47A30

Pages:  19$-$32     

Volume  66 ,  Issue  1 ,  2014