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Lp-Lq multipliers on commutative hypergroups

Vishvesh Kumar (UGent) and Michael Ruzhansky (UGent)
(2023) JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY. 115(3). p.375-395
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Abstract
The main purpose of this paper is to prove Hormander's L-p-L-q boundedness of Fourier multipliers on commutative hypergroups. We carry out this objective by establishing the Paley inequality and Hausdorff-Young-Paley inequality for commutative hypergroups. We show the L-p-L-q boundedness of the spectral multipliers for the generalised radial Laplacian by examining our results on Chebli-Trimeche hypergroups. As a consequence, we obtain embedding theorems and time asymptotics for the L-p-L-q norms of the heat kernel for generalised radial Laplacian.
Keywords
Ghent Analysis & PDE center, Chebli-Trimeche hypergroups, Fourier multipliers, spectral multipliers, Jacobi transform, Hankel transform, generalised radial Laplacian, LP-FOURIER MULTIPLIERS, L-P, HARDY-LITTLEWOOD, PALEY INEQUALITIES, OPERATOR, THEOREM, SPACES

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MLA
Kumar, Vishvesh, and Michael Ruzhansky. “Lp-Lq Multipliers on Commutative Hypergroups.” JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, vol. 115, no. 3, 2023, pp. 375–95, doi:10.1017/S1446788723000125.
APA
Kumar, V., & Ruzhansky, M. (2023). Lp-Lq multipliers on commutative hypergroups. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 115(3), 375–395. https://doi.org/10.1017/S1446788723000125
Chicago author-date
Kumar, Vishvesh, and Michael Ruzhansky. 2023. “Lp-Lq Multipliers on Commutative Hypergroups.” JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY 115 (3): 375–95. https://doi.org/10.1017/S1446788723000125.
Chicago author-date (all authors)
Kumar, Vishvesh, and Michael Ruzhansky. 2023. “Lp-Lq Multipliers on Commutative Hypergroups.” JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY 115 (3): 375–395. doi:10.1017/S1446788723000125.
Vancouver
1.
Kumar V, Ruzhansky M. Lp-Lq multipliers on commutative hypergroups. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY. 2023;115(3):375–95.
IEEE
[1]
V. Kumar and M. Ruzhansky, “Lp-Lq multipliers on commutative hypergroups,” JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, vol. 115, no. 3, pp. 375–395, 2023.
@article{01HP4Q5DX9MQFS7GA04CY2ZR3D,
  abstract     = {{The main purpose of this paper is to prove Hormander's L-p-L-q boundedness of Fourier multipliers on commutative hypergroups. We carry out this objective by establishing the Paley inequality and Hausdorff-Young-Paley inequality for commutative hypergroups. We show the L-p-L-q boundedness of the spectral multipliers for the generalised radial Laplacian by examining our results on Chebli-Trimeche hypergroups. As a consequence, we obtain embedding theorems and time asymptotics for the L-p-L-q norms of the heat kernel for generalised radial Laplacian.}},
  author       = {{Kumar, Vishvesh and Ruzhansky, Michael}},
  issn         = {{1446-7887}},
  journal      = {{JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY}},
  keywords     = {{Ghent Analysis & PDE center,Chebli-Trimeche hypergroups,Fourier multipliers,spectral multipliers,Jacobi transform,Hankel transform,generalised radial Laplacian,LP-FOURIER MULTIPLIERS,L-P,HARDY-LITTLEWOOD,PALEY INEQUALITIES,OPERATOR,THEOREM,SPACES}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{375--395}},
  title        = {{Lp-Lq multipliers on commutative hypergroups}},
  url          = {{http://doi.org/10.1017/S1446788723000125}},
  volume       = {{115}},
  year         = {{2023}},
}
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