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.
Citation
Qingyan Wu. Zunwei Fu. "Boundedness of Hausdorff operators on Hardy spaces in the Heisenberg group." Banach J. Math. Anal. 12 (4) 909 - 934, October 2018. https://doi.org/10.1215/17358787-2018-0006
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