L^p-Fourier transforms on nilpotent Lie groups and solvable Lie groups acting on Siegel domains

Junko Inoue

Vol. 155 (1992), No. 2, 295–318

DOI: 10.2140/pjm.1992.155.295

Abstract

We study Fourier transforms of L^p-functions (1 < p ≤ 2) on nilpotent Lie groups and affine automorphism groups of Siegel domains. We get an estimate for the norm of the L^p-Fourier transform for certain classes of nilpotent Lie groups. For affine automorphism groups, which are nonunimodular, we give an explicit definition of L^p-Fourier transform, and obtain an estimate for the norm.

Mathematical Subject Classification 2000

Primary: 22E25

Secondary: 22E30, 32M05

Milestones

Received: 21 June 1990

Revised: 14 August 1991

Published: 1 October 1992