Hausdorff operators associated with the Opdam–Cherednik transform in Lebesgue spaces

Shyam Swarup Mondal, Anirudha Poria*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

In this paper, we introduce the Hausdorff operator associated with the Opdam–Cherednik transform and study the boundedness of this operator in various Lebesgue spaces. In particular, we prove the boundedness of the Hausdorff operator in Lebesgue spaces, in grand Lebesgue spaces, and in quasi-Banach spaces that are associated with the Opdam–Cherednik transform. Also, we give necessary and sufficient conditions for the boundedness of the Hausdorff operator in these spaces.

Original languageEnglish
Article number31
JournalJournal of Pseudo-Differential Operators and Applications
Volume13
Issue number3
DOIs
Publication statusPublished - Sept 2022

Keywords

  • Grand Lebesgue spaces
  • Hausdorff operator
  • Lebesgue spaces
  • Opdam–Cherednik transform
  • Quasi-Banach spaces

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