Riesz transforms, fractional power and functional calculus of Schrödinger operators on weighted \(L^p\)-spaces
type: Item
instance of: scholarly article
title: Riesz transforms, fractional power and functional calculus of Schrödinger operators on weighted \(L^p\)-spaces
zbMATH Open document ID: 1280.47043
author: Joyce Assaad
published in: Journal of Mathematical Analysis and Applications
publication date: 2013-04-22T00:00:00Z
review text: The Schrödinger operator \(-\Delta+V^{+}-V^{-}\) on the weighted Lebesgue space \(L^p(\mathbb{R}^N, w\,dx)\), where \(N\geq 3\) and \(w\) is a weight in some Muckenhoupt class, is considered in the paper. The author studies the boundedness of Riesz transform type operators \(\nabla A^{-1/2}\) and \(|V|^{1/2}A^{-1/2}\) on \(L^p(\mathbb{R}^N, wdx)\). The results extend those of \textit{P. Auscher} and \textit{B. Ben Ali} [Ann. Inst. Fourier 57, No.~6, 1975--2013 (2007; Zbl 1161.35003)], \textit{The Anh Bui} [Differ. Integral Equ. 23, No.~9--10, 811--826 (2010; Zbl 1240.42034)], \textit{J. Assaad} and \textit{E. M. Ouhabaz} [J. Geom. Anal. 22, No.~4, 1108--1136 (2012; Zbl 1259.58006)].
reviewed by: Stepan Agop Tersian
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 42B37
Mathematics Subject Classification ID: 35J10
zbMATH DE Number: 6156117
zbMATH Keywords: Riesz transforms
zbMATH Keywords: Schrödinger operators
zbMATH Keywords: fractional powers
zbMATH Keywords: functional calculus
zbMATH Keywords: off-diagonal estimates
zbMATH Keywords: Muckenhoupt class
zbMATH Keywords: reverse Hölder class
MaRDI profile type: Publication
full work available at URL: j.jmaa.2013.01.024
OpenAlex ID: W1979730148
DOI: 10.1016/J.JMAA.2013.01.024
description: scientific article; zbMATH DE number 6156117