Two-weight norm inequalities for the rough fractional integrals
type: Item
instance of: scholarly article
title: Two-weight norm inequalities for the rough fractional integrals
zbMATH Open document ID: 1007.42014
DOI: 10.1155/S0161171201003982
author: Chin-Cheng Lin
author: Yong Ding
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2003-03-07T00:00:00Z
full work available at URL: https://eudml.org/doc/49829
review text: Suppose that \(0<\alpha<n\), \(\Omega(x)\) is a function homogeneous of degree zero in \({\mathbb R}^n\) and its restriction to the unit sphere \(S^{n-1}\) is in \(L^s(S^{n-1})\) for some \(s>1\). Define the fractional integral operator \(T_{\Omega ,\alpha }\) and the fractional maximal operator \(M_{\Omega ,\alpha}\), respectively, by \[ T_{\Omega ,\alpha }f(x)=\int_{{\mathbb R}^n} \frac {\Omega (x-y)}{|x-y|^{n-\alpha}}f(y) dy \] and \[ M_{\Omega ,\alpha }f(x)=\sup_{r>0} \frac 1{r^{n-\alpha }} \int_{|x-y|<r} |\Omega (x-y)||f(y)|dy. \] In this paper, the authors establish the weighted \((L^p,L^q)\)-boundedness of \(T_{\Omega ,\alpha }\) and \(M_{\Omega ,\alpha}\) with two different weights.
Mathematics Subject Classification ID: 42B20
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 26A33
zbMATH DE Number: 1751242
zbMATH Keywords: fractional integral
zbMATH Keywords: fractional maximal operator
zbMATH Keywords: rough kernel
zbMATH Keywords: weight
zbMATH Keywords: boundedness
reviewed by: Dachun Yang
MaRDI profile type: Publication
OpenAlex ID: W1980823703
description: scientific article; zbMATH DE number 1751242