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The unboundedness of Hausdorff operators on Quasi-Banach spaces
  • Weichao Guo,
  • Jianmiao Ruan,
  • Guoping Zhao
Weichao Guo
Jimei University
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Jianmiao Ruan
Zhejiang International Studies University
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Guoping Zhao
Xiamen University of Technology
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Peer review status:UNDER REVIEW

27 Jun 2020Submitted to Mathematical Methods in the Applied Sciences
04 Jul 2020Assigned to Editor
04 Jul 2020Submission Checks Completed
11 Jul 2020Reviewer(s) Assigned

Abstract

In this note, we show that the Hausdorff operator $H_{\Phi}$ is unbounded on a large family of Quasi-Banach spaces, unless $H_{\Phi}$ is a zero operator.