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arXiv · 1806.11296

Complementation of the subspace of radial multipliers in the space of Fourier multipliers on $\mathbb{R}^n$

Cédric Arhancet·Christoph Kriegler
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Abstract

In this short note, we prove that the subspace of radial multipliers is contractively complemented in the space of Fourier multipliers on the Bochner space $\mathrm{L}^p(\mathbb{R}^n,X)$ where $X$ is a Banach space and where $1 \leq p <\infty$. Moreover, if $X = \mathbb{C}$, then this complementation preserves the positivity of multipliers.

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Cédric Arhancet, Christoph Kriegler. 2018-06-29. Complementation of the subspace of radial multipliers in the space of Fourier multipliers on $\mathbb{R}^n$. https://arxiv.org/abs/1806.11296

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