L^p-L^q Multipliers on commutative hypergroups

2021/08/02 by Vishvesh Kumar, Michael Ruzhansky, Kumar, Vishvesh +1
Mathematics · #42B10 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Primary 43A62 #Secondary 42A45 #math.FA #msc:42A45 #msc:42B10 #msc:43A62

paper · pdf · doi:10.48550/arxiv.2108.01146

30 pages, comments are welcome. arXiv admin note: text overlap with arXiv:2101.03416

arxiv created 2021/08/02 · openalex publication_date 2021/08/02 · arxiv updated 2021/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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• L^p-L^q boundedness of (k, a)-Fourier multipliers with applications to Nonlinear equations

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