Please use this identifier to cite or link to this item:
http://hdl.handle.net/2445/183656
Title: | Idempotent Fourier multipliers acting contractively on $H^{P}$ spaces |
Author: | Brevig, Ole Fredrik Ortega Cerdà, Joaquim Seip, Kristian |
Keywords: | Anàlisi harmònica Funcions de variables complexes Harmonic analysis Functions of complex variables |
Issue Date: | 27-Dec-2021 |
Publisher: | Springer Verlag |
Abstract: | 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 $p=2,4, \ldots, 2(n+1)$. |
Note: | Reproducció del document publicat a: https://doi.org/10.1007/s00039-021-00586-0 |
It is part of: | Geometric and Functional Analysis, 2021, vol. 31, num. 6, p. 1377-1413 |
URI: | http://hdl.handle.net/2445/183656 |
Related resource: | https://doi.org/10.1007/s00039-021-00586-0 |
ISSN: | 1016-443X |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
715847.pdf | 639.78 kB | Adobe PDF | View/Open |
This item is licensed under a Creative Commons License