1 results
$\boldsymbol {L}^{\boldsymbol {p}}$–
$\boldsymbol {L}^{\boldsymbol {q}}$ MULTIPLIERS ON COMMUTATIVE HYPERGROUPS
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 115 / Issue 3 / December 2023
- Published online by Cambridge University Press:
- 18 October 2023, pp. 375-395
- Print publication:
- December 2023
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- Article
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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.
