# name
Idempotent Fourier multipliers acting contractively on $H^{P}$ spaces

# metadata.dc.description.abstract[].value
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 $p=2,4, \ldots, 2(n+1)$.

# metadata.dc.relation.ispartof[].value
Geometric and Functional Analysis, 2021, vol. 31, num. 6, p. 1377-1413

# metadata.dc.source[].value
Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
Idempotent Fourier multipliers acting contractively on $H^{P}$ spaces