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

Shyam Swarup Mondal; Anirudha Poria

doi:10.1007/s11868-022-00462-x

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

Shyam Swarup Mondal, Anirudha Poria^*

^*Corresponding author for this work

Department of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

5 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 language	English
Article number	31
Journal	Journal of Pseudo-Differential Operators and Applications
Volume	13
Issue number	3
DOIs	https://doi.org/10.1007/s11868-022-00462-x
Publication status	Published - Sept 2022

Keywords

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

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10.1007/s11868-022-00462-x

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Mondal, S. S., & Poria, A. (2022). Hausdorff operators associated with the Opdam–Cherednik transform in Lebesgue spaces. Journal of Pseudo-Differential Operators and Applications, 13(3), Article 31. https://doi.org/10.1007/s11868-022-00462-x

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title = "Hausdorff operators associated with the Opdam–Cherednik transform in Lebesgue spaces",

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.",

keywords = "Grand Lebesgue spaces, Hausdorff operator, Lebesgue spaces, Opdam–Cherednik transform, Quasi-Banach spaces",

author = "Mondal, {Shyam Swarup} and Anirudha Poria",

note = "Funding Information: The first author gratefully acknowledges the support provided by IIT Guwahati, Government of India. The second author is deeply indebted to Prof. Nir Lev for several fruitful discussions and generous comments. The authors wish to thank the anonymous referee for valuable comments and suggestions that helped to improve the quality of the paper. Funding Information: Research supported by ERC Starting Grant No. 713927. Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",

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doi = "10.1007/s11868-022-00462-x",

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AU - Mondal, Shyam Swarup

AU - Poria, Anirudha

N1 - Funding Information: The first author gratefully acknowledges the support provided by IIT Guwahati, Government of India. The second author is deeply indebted to Prof. Nir Lev for several fruitful discussions and generous comments. The authors wish to thank the anonymous referee for valuable comments and suggestions that helped to improve the quality of the paper. Funding Information: Research supported by ERC Starting Grant No. 713927. Publisher Copyright: © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

PY - 2022/9

Y1 - 2022/9

N2 - 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.

AB - 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.

KW - Grand Lebesgue spaces

KW - Hausdorff operator

KW - Lebesgue spaces

KW - Opdam–Cherednik transform

KW - Quasi-Banach spaces

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JF - Journal of Pseudo-Differential Operators and Applications

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ER -

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

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Keywords

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