Banach Journal of Mathematical Analysis

Boundedness of Hausdorff operators on Hardy spaces in the Heisenberg group

Qingyan Wu and Zunwei Fu

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Abstract

In the setting of the Heisenberg group, we define weighted Hardy spaces by means of their atomic characterization, and we establish the (sharp) boundedness of Hausdorff operators on power-weighted Hardy spaces. Moreover, we obtain sufficient and necessary conditions for the boundedness of Hausdorff operators on local Hardy spaces in the Heisenberg group.

Article information

Source
Banach J. Math. Anal., Volume 12, Number 4 (2018), 909-934.

Dates
Received: 23 October 2017
Accepted: 5 March 2018
First available in Project Euclid: 22 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1529632824

Digital Object Identifier
doi:10.1215/17358787-2018-0006

Mathematical Reviews number (MathSciNet)
MR3858754

Zentralblatt MATH identifier
06946296

Subjects
Primary: 47G10: Integral operators [See also 45P05]
Secondary: 22E25: Nilpotent and solvable Lie groups 26D15: Inequalities for sums, series and integrals 42B30: $H^p$-spaces

Keywords
Hausdorff operator Heisenberg group Hardy space power weight local Hardy space

Citation

Wu, Qingyan; Fu, Zunwei. Boundedness of Hausdorff operators on Hardy spaces in the Heisenberg group. Banach J. Math. Anal. 12 (2018), no. 4, 909--934. doi:10.1215/17358787-2018-0006. https://projecteuclid.org/euclid.bjma/1529632824


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