Generalized Fourier transform on Ch\'ebli-Trim\'eche hypergroups
Chokri Abdelkefi, Abdessattar Jemai
TL;DR
This paper extends the Fourier transform framework to Chébli-Triméche hypergroups, establishing inequalities and integrability properties, with specific focus on Jacobi hypergroups and Besov spaces.
Contribution
It introduces a generalized Fourier transform on Chébli-Triméche hypergroups and proves Hardy-Littlewood inequalities, analyzing integrability on Besov-type spaces for Jacobi hypergroups.
Findings
Proved Hardy-Littlewood inequality for the generalized Fourier transform.
Studied integrability of the transform on Besov-type spaces.
Established results specifically for Jacobi hypergroups.
Abstract
In this paper, we prove the Hardy-Littlewood inequality for the generalized Fourier transform on Ch\'ebli-Trim\'eche hypergroups and we study in the particular case of the Jacobi hypergroup the integrability of this transform on Besov-type spaces.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Advanced Harmonic Analysis Research · Advanced Algebra and Geometry