A note on twisted discrete singular Radon transforms
type: Item
instance of: scholarly article
title: A note on twisted discrete singular Radon transforms
zbMATH Open document ID: 1227.44001
published in: Mathematical Research Letters
publication date: 2011-08-09T00:00:00Z
full work available at URL: https://arxiv.org/abs/1005.4426
review text: The author considers three types of discrete operators stemming from singular Radon transforms. She first extends an \(\ell^p\) result for translation invariant discrete singular Radon transforms to a class of twisted operators including an additional oscillatory component, via a simple method of descent argument. We note an \(\ell^2\) bound for quasi-translation invariant discrete twisted Radon transforms. Finally, the author extends an existing \(\ell^2\) bound for a closely related non-translation invariant discrete oscillatory integral operator with singular kernel to an \(\ell^p\) bound for all \(1< p< \infty\). This requires an intricate induction argument involving layers of decompositions of the operator according to the Diophantine properties of the coefficients of its polynomial phase function.
reviewed by: Kun Soo Chang
Mathematics Subject Classification ID: 44A12
zbMATH DE Number: 5937402
zbMATH Keywords: singular Radon transforms
zbMATH Keywords: twisted operators
zbMATH Keywords: quasi-translation invariant
zbMATH Keywords: oscillatory integral operator
zbMATH Keywords: Diophantine properties
zbMATH Keywords: polynomial phase function
author: Lillian Beatrix Pierce
MaRDI profile type: Publication
arXiv ID: 1005.4426
OpenAlex ID: W1965365096
DOI: 10.4310/MRL.2010.V17.N4.A10
description: scientific article