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Sharp weighted bounds for fractional integral operators

By Michael T. Lacey, Kabe Moen, Carlos Pérez and Rodolfo H. Torres

Abstract

AbstractThe relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp bounds are obtained for both the fractional integral operators and the associated fractional maximal functions. As an application improved Sobolev inequalities are obtained. Some of the techniques used include a sharp off-diagonal version of the extrapolation theorem of Rubio de Francia and characterizations of two-weight norm inequalities

Publisher: Published by Elsevier Inc.
Year: 2010
DOI identifier: 10.1016/j.jfa.2010.02.004
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