Abstract
AbstractThe 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.
Publisher
Cambridge University Press (CUP)