Hausdorff operators on the Heisenberg group |
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| Authors: | Jiu Hua Guo Li Jing Sun Fa You Zhao |
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| Institution: | 1. Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China;
2. Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA;
3. Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China |
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| Abstract: | This paper is devoted to the high-dimensional and multilinear Hausdorff operators on the Heisenberg group Hn. The sharp bounds for the strong type (p, p) (1 ≤ p ≤ ∞) estimates of n-dimensional Hausdorff operators on Hn are obtained. The sharp bounds for strong (p, p) estimates are further extended to multilinear cases. As an application, we derive the sharp constant for the multilinear Hardy operator on Hn. The weak type (p, p) (1 ≤ p ≤ ∞) estimates are also obtained. |
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| Keywords: | Hausdorff operator Heisenberg group multilinear sharp estimate |
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