\(L^p\)-norms of periodizations over integer lattices
type: Item
instance of: scholarly article
title: \(L^p\)-norms of periodizations over integer lattices
zbMATH Open document ID: 1237.11030
author: Oleg Kovrizhkin
published in: Journal of Mathematical Analysis and Applications
publication date: 2011-10-21T00:00:00Z
review text: The periodizations with respect to a rotated integer lattice \(g_\rho (x)=\sum_{\nu \in \mathbb{Z}^d}f(\rho (x-\nu ))\) corresponding to \(\rho\in \text{SO}(d)\) of the functions \(f\in L^1(\mathbb{R}^d)\) appear in the Steinhaus tiling set problem. In this note the author presents an estimate concerning the mixed norm \(\| g\|_{p,s}=\left( \int_{\rho \in\text{SO}(d)}\| g_\rho -\hat g(0) \|_p^s\, d\rho \right)^{1/s}\).
reviewed by: Nicolae Cotfas
Mathematics Subject Classification ID: 11H06
zbMATH DE Number: 5960930
zbMATH Keywords: periodizations
zbMATH Keywords: integer lattices
MaRDI profile type: Publication
full work available at URL: j.jmaa.2011.07.068
OpenAlex ID: W2020879701
cites work: Q5283836
cites work: On the Steinhaus tiling problem
cites work: On the \(L^2\)-norm of periodizations of functions
DOI: 10.1016/J.JMAA.2011.07.068
description: scientific article; zbMATH DE number 5960930