Open Access
July 2017 Weighted Herz space estimates for Hausdorff operators on the Heisenberg group
Jianmiao Ruan, Dashan Fan, Qingyan Wu
Banach J. Math. Anal. 11(3): 513-535 (July 2017). DOI: 10.1215/17358787-2017-0004


In this article, we study the Hausdorff operator, defined via a general linear mapping A, on weighted Herz spaces in the setting of the Heisenberg group. Under some assumptions on the mapping A, we establish its sharp boundedness on power-weighted Herz spaces and power-weighted Lebesgue spaces in the Heisenberg group. Our proof is heavily based on the block decomposition of the Herz space, which is quite different from any other function spaces. Our results extend and improve some existing theorems.


Download Citation

Jianmiao Ruan. Dashan Fan. Qingyan Wu. "Weighted Herz space estimates for Hausdorff operators on the Heisenberg group." Banach J. Math. Anal. 11 (3) 513 - 535, July 2017.


Received: 7 July 2016; Accepted: 18 August 2016; Published: July 2017
First available in Project Euclid: 19 April 2017

zbMATH: 1370.42020
MathSciNet: MR3679894
Digital Object Identifier: 10.1215/17358787-2017-0004

Primary: 42B35
Secondary: 22E25 , 42B30 , 46E30

Keywords: Hausdorff operator , Heisenberg group , Herz space , weight

Rights: Copyright © 2017 Tusi Mathematical Research Group

Vol.11 • No. 3 • July 2017
Back to Top