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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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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.

Peer review status:ACCEPTED

27 Jun 2020Submitted to Mathematical Methods in the Applied Sciences
04 Jul 2020Submission Checks Completed
04 Jul 2020Assigned to Editor
11 Jul 2020Reviewer(s) Assigned
18 Oct 2020Review(s) Completed, Editorial Evaluation Pending
23 Oct 2020Editorial Decision: Revise Major
20 Jan 20211st Revision Received
20 Jan 2021Assigned to Editor
20 Jan 2021Submission Checks Completed
24 Jan 2021Reviewer(s) Assigned
09 Feb 2021Review(s) Completed, Editorial Evaluation Pending
10 Apr 2021Editorial Decision: Revise Major
07 Jul 20212nd Revision Received
07 Jul 2021Assigned to Editor
07 Jul 2021Submission Checks Completed
14 Jul 2021Review(s) Completed, Editorial Evaluation Pending
15 Jul 2021Editorial Decision: Accept