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Multilinear Hausdorff operators and their best constants |
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| Authors: | Jie Cheng Chen Da Shan Fan Chun Jie Zhang |
| Institution: | 1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, P. R. China 2. Department of Mathematics, Zhejiang University, Hangzhou, 310027, P. R. China 3. Department of Mathematics, University of Wisconsin-Milwaukee, Milwaukee, WI, 53201, USA 4. School of Science, Hangzhou Dianzi University, Hangzhou, 310018, P. R. China |
| Abstract: | In this paper, we study two different extensions of the Hausdorff operator to the multilinear case. Boundedness on Lebesgue spaces and Herz spaces is obtained. The bound on the Lebesgue space is optimal. Our results are substantial extensions of some known results on Multilinear high dimensional Hardy operator. |
| Keywords: | Hausdorff operator multilinear Herz space sharp bounds |
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