Characterization of Multipliers on Hypergroups

Kumar, Vishvesh; Kumar, N. Shravan; Sarma, Ritumoni

doi:10.1007/s40306-020-00379-x

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Cited by 2 publications

(2 citation statements)

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“…A Fourier multiplier commutes with the translation operators. In fact, the Fourier multipliers can be characterised using translation operators [12,34,38].…”

Section: 3mentioning

confidence: 99%

– Multipliers on Commutative Hypergroups

KUMAR,

RUZHANSKY

2023

J. Aust. Math. Soc.

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The main purpose of this paper is to prove Hörmander’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 Chébli–Trimèche 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.

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“…A Fourier multiplier commutes with the translation operators. In fact, the Fourier multipliers can be characterised using translation operators [12,34,38].…”

Section: 3mentioning

confidence: 99%

– Multipliers on Commutative Hypergroups

KUMAR,

RUZHANSKY

2023

J. Aust. Math. Soc.

Self Cite

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“…A Fourier multiplier commutes with the translation operators. In fact, the Fourier multipliers can be characterized using translation operators [46,13,38].…”

Section: 2mentioning

confidence: 99%

$L^p$-$L^q$ Multipliers on commutative hypergroups

Kumar,

Ruzhansky

2021

Preprint

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The main purpose of this paper is to prove Hörmander's L p -L q boundedness of Fourier multipliers on commutative hypergroups. We carry out this objective by establishing 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 Chébli-Trimèche 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. Finally, we present applications of the obtained results to study the well-posedness of nonlinear partial differential equations.

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Characterization of Multipliers on Hypergroups

Cited by 2 publications

References 11 publications

– Multipliers on Commutative Hypergroups

– Multipliers on Commutative Hypergroups

$L^p$-$L^q$ Multipliers on commutative hypergroups

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