Brevig, Ole FredrikOrtega Cerdà, JoaquimSeip, Kristian2022-03-012022-03-012021-12-271016-443Xhttps://hdl.handle.net/2445/183656We 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 $p=2,4, \ldots, 2(n+1)$.37 p.application/pdfengcc by (c) Brevik, Ole Fredrik, 2021http://creativecommons.org/licenses/by/3.0/es/Anàlisi harmònicaFuncions de variables complexesHarmonic analysisFunctions of complex variablesinfo:eu-repo/semantics/article7158472022-03-01info:eu-repo/semantics/openAccess