caa a22 4500 60546233X CHVBK 20210128100247.0 cr unu---uuuuu 210128e20151101xx s 000 0 eng 10.1007/s10114-015-5109-4 doi (NATIONALLICENCE)springer-10.1007/s10114-015-5109-4 Hausdorff operators on the Heisenberg group [Elektronische Daten] [Jiu Guo, Li Sun, Fa Zhao] This paper is devoted to the high-dimensional and multilinear Hausdorff operators on the Heisenberg group H n . The sharp bounds for the strong type (p, p) (1 ≤ p ≤ ∞) estimates of n-dimensional Hausdorff operators on H n 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 H n . The weak type (p, p) (1 ≤ p≤∞) estimates are also obtained. Keywords Hausdorff operator, Heisenberg group, multilinear, sharp estimate Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 Hausdorff operator nationallicence Heisenberg group nationallicence multilinear nationallicence sharp estimate nationallicence Guo Jiu Department of Mathematics, Shanghai University, 200444, Shanghai, P. R. China aut Sun Li Department of Mathematical Sciences, University of Wisconsin-Milwaukee, 53201, Milwaukee, WI, USA aut Zhao Fa Department of Mathematics, Shanghai University, 200444, Shanghai, P. R. China aut Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/11(2015-11-01), 1703-1714 1439-8516 31:11<1703 2015 31 10114 https://doi.org/10.1007/s10114-015-5109-4 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10114-015-5109-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Guo Jiu Department of Mathematics, Shanghai University, 200444, Shanghai, P. R. China aut NATIONALLICENCE 700 1- Sun Li Department of Mathematical Sciences, University of Wisconsin-Milwaukee, 53201, Milwaukee, WI, USA aut NATIONALLICENCE 700 1- Zhao Fa Department of Mathematics, Shanghai University, 200444, Shanghai, P. R. China aut NATIONALLICENCE 773 0- Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/11(2015-11-01), 1703-1714 1439-8516 31:11<1703 2015 31 10114