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# Collection Frontiers of Operator Theory / Frontières de la théorie des opérateurs

Organizer(s) Badea, Catalin ; Bayart, Frédéric ; Gallardo-Gutiérrez, Eva A. ; Grivaux, Sophie ; Lefèvre, Pascal
Date(s) 11/29/21 - 12/3/21
00:00:00 / 00:00:00
1 5

## Idempotent Fourier multipliers acting contractively on Hardy space

We describe the idempotent Fourier multipliers that act contractively on $H^{p}$ spaces of the $d$-dimensional torus $\mathbb{T}^{d}$ for $d \geq 1$ and $1 \leq p \leq \infty$. When $p$ is not an even integer, such multipliers are just restrictions of contractive idempotent multipliers on $L^{p}$ spaces, which in turn can be described by suitably combining results of Rudin and Andô. When $p=2(n+1)$, with $n$ a positive integer, contractivity depends in an interesting geometric way on $n, d$, and the dimension of the set of frequencies associated with the multiplier. Our results allow us to construct a linear operator that is densely defined on $H^{p}\left(\mathbb{T}^{\infty}\right)$ for every $1 \leq p \leq \infty$ and that extends to a bounded operator if and only if $p=2,4, \ldots, 2(n+1)$. The talk is based on joint work with Ole Fredrik Brevig and Joaquim Ortega-Cerdà.

### Citation data

• DOI 10.24350/CIRM.V.19855803
• Cite this video Seip Kristian (11/29/21). Idempotent Fourier multipliers acting contractively on Hardy space. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19855803
• URL https://dx.doi.org/10.24350/CIRM.V.19855803

### Bibliography

• BREVIG, Ole Fredrik, ORTEGA-CERDÀ, Joaquim, et SEIP, Kristian. Idempotent Fourier multipliers acting contractively on $H^ p$ spaces. arXiv preprint arXiv:2103.16186, 2021. - https://arxiv.org/abs/2103.16186v2

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