Titchmarsh theorems for Fourier transforms of Hölder-Lipschitz functions on compact homogeneous manifolds

2017/02/19 by Radouan Daher, Daher, Radouan, Michael Ruzhansky +2
Mathematics · #Advanced Harmonic Analysis Research #Mathematical Analysis and Transform Methods #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1702.05731

Abstract

In this paper we extend classical Titchmarsh theorems on the Fourier transform of Hölder-Lipschitz functions to the setting of compact homogeneous manifolds. As an application, we derive a Fourier multiplier theorem for L²-Hölder-Lipschitz spaces on compact Lie groups. We also derive conditions and a characterisation for Dini-Lipschitz classes on compact homogeneous manifolds in terms of the behaviour of their Fourier coefficients.

Citations

• Layer potentials, Kac's problem, and refined Hardy inequality on homogeneous Carnot groups

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