Vector-valued inequalities, factorization, and extrapolation for a family of rough operators
type: Item
instance of: scholarly article
title: Vector-valued inequalities, factorization, and extrapolation for a family of rough operators
zbMATH Open document ID: 0811.47050
author: David K. Watson
published in: Journal of Functional Analysis
publication date: 1995-05-01T00:00:00Z
review text: The author proves very general weighted norm inequalities for rough maximal and singular integral operators whose kernels satisfy some common Fourier transform decay estimates. Examples include homogeneous singular integral operators with kernels which do not necessarily satisfy a Dini condition as well as several operators whose measures are supported on lower dimensional sets, such as the discrete spherical maximal operator and the Hilbert transform along a homogeneous curve. The weights are shown to satisfy analogues of Jones' factorization theorem and Rubio de Francia's extrapolation theorem, and so are complete with respect to these important properties. The author also obtains the corresponding weighted vector-valued inequalities for these operators and for the maximal operator associated with a starlike set.
Mathematics Subject Classification ID: 47G10
zbMATH DE Number: 599787
zbMATH Keywords: weighted norm inequalities for rough maximal and singular integral operators
zbMATH Keywords: kernels
zbMATH Keywords: Fourier transform decay estimates
zbMATH Keywords: homogeneous singular integral operators
zbMATH Keywords: Dini condition
zbMATH Keywords: discrete spherical maximal operator
zbMATH Keywords: Hilbert transform along a homogeneous curve
zbMATH Keywords: Jones' factorization theorem
zbMATH Keywords: Rubio de Francia's extrapolation theorem
zbMATH Keywords: weighted vector-valued inequalities
zbMATH Keywords: maximal operator associated with a starlike set
MaRDI profile type: Publication
full work available at URL: jfan.1994.1053
OpenAlex ID: W2057532929
DOI: 10.1006/JFAN.1994.1053
description: scientific article; zbMATH DE number 599787