Banach Journal of Mathematical Analysis

Weighted Herz space estimates for Hausdorff operators on the Heisenberg group

Jianmiao Ruan, Dashan Fan, and Qingyan Wu

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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.

Article information

Banach J. Math. Anal., Volume 11, Number 3 (2017), 513-535.

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

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Zentralblatt MATH identifier

Primary: 42B35: Function spaces arising in harmonic analysis
Secondary: 42B30: $H^p$-spaces 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 22E25: Nilpotent and solvable Lie groups

Hausdorff operator Herz space Heisenberg group weight


Ruan, Jianmiao; Fan, Dashan; Wu, Qingyan. Weighted Herz space estimates for Hausdorff operators on the Heisenberg group. Banach J. Math. Anal. 11 (2017), no. 3, 513--535. doi:10.1215/17358787-2017-0004.

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