Fractional integrals and \(A_p\)-weights: a sharp estimate
type: Item
instance of: scholarly article
title: Fractional integrals and \(A_p\)-weights: a sharp estimate
zbMATH Open document ID: 1180.26001
author: Teresa Alberico
author: Andrea Cianchi
author: Carlo Sbordone
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2009-11-25T00:00:00Z
review text: This paper deals with an inequality with an \(A_p\) weight for Riesz potential of a function \(f: \mathbb{R}^n\to \mathbb{R}\) defined by \[ I_\alpha f(x)= \int_{\mathbb{R}^n} {f(y)\over |x-y|^{n-\alpha}}\,dy\qquad\text{for }x\in\mathbb{R}^n. \] The constant in the relevant inequality is known to depend on the \(A_p\) constant of the weight. The authors find the exact form of this dependence. In particular, they exhibit the optimal exponent for the \(A_p\) constant of the weight.
reviewed by: Som Prakash Goyal
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 26D10
zbMATH DE Number: 5638292
zbMATH Keywords: fractional integrals
zbMATH Keywords: Riesz potentials
zbMATH Keywords: sharp estimate
MaRDI profile type: Publication
full work available at URL: j.crma.2009.09.001
OpenAlex ID: W2002884998
cites work: Beltrami operators in the plane
cites work: Estimates for Operator Norms on Weighted Spaces and Reverse Jensen Inequalities
cites work: Weighted norm inequalities for maximal functions and singular integrals
cites work: A Note on a Weighted Sobolev Inequality
cites work: The local regularity of solutions of degenerate elliptic equations
cites work: On Certain Convolution Inequalities
cites work: Q3995421
cites work: Weighted Norm Inequalities for the Hardy Maximal Function
cites work: Weighted Norm Inequalities for Fractional Integrals
cites work: The sharp bound for the Hilbert transform on weighted Lebesgue spaces in terms of the classical A p characteristic
cites work: The sharp weighted bound for the Riesz transforms
cites work: Heating of the Ahlfors-Beurling operator: weakly quasiregular maps on the plane are quasiregular
cites work: Q3142876
DOI: 10.1016/J.CRMA.2009.09.001
description: scientific article; zbMATH DE number 5638292