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arXiv · 1702.05731

Titchmarsh theorems for Fourier transforms of H\"older-Lipschitz functions on compact homogeneous manifolds

Radouan Daher·Julio Delgado·Michael Ruzhansky
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Abstract

In this paper we extend classical Titchmarsh theorems on the Fourier transform of H\"older-Lipschitz functions to the setting of compact homogeneous manifolds. As an application, we derive a Fourier multiplier theorem for $L^2$-H\"older-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.

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Radouan Daher, Julio Delgado, Michael Ruzhansky. 2017-02-19. Titchmarsh theorems for Fourier transforms of H\"older-Lipschitz functions on compact homogeneous manifolds. https://arxiv.org/abs/1702.05731

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