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arXiv · 1605.07868

Fourier multipliers and group von Neumann algebras

Rauan Akylzhanov·Michael Ruzhansky
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Abstract

In this paper we establish the $L^p$-$L^q$ boundedness of Fourier multipliers on locally compact separable unimodular groups for the range of indices $1<p\leq 2 \leq q<\infty$. Our approach is based on the operator algebras techniques. The result depends on a version of the Hausdorff-Young-Paley inequality that we establish on general locally compact separable unimodular groups. In particular, the obtained result implies the corresponding H\"ormander's Fourier multiplier theorem on $\mathbb{R}^{n}$ and the corresponding known results for Fourier multipliers on compact Lie groups.

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Rauan Akylzhanov, Michael Ruzhansky. 2016-05-25. Fourier multipliers and group von Neumann algebras. https://doi.org/10.1016/j.crma.2016.05.010

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