Multilinear Hausdorff operators and their best constants

Authors
Chen, Jie Cheng Fan, Da Shan Zhang, Chun Jie
Citation
Chen, Jie Cheng et al., Multilinear Hausdorff operators and their best constants, Acta mathematica Sinica. English series (Print) , 28(8), 2012, pp. 1521-1530
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
28
Issue
8
Year of publication
2012
Pages
1521 - 1530
Database
ACNP
SICI code
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.