Sharp weighted bounds for fractional integral operators

Details Sharp weighted bounds for fractional integral operators Sharp weighted bounds for fractional integral operators

2009-05-23

arxiv.org/abs/0905.3839v2

Mathematics

Classical Analysis and ODEs

v2: changes made to reflect referee's report. Final version of the paper. To appear in J Func Anal

Scientific paper

The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp boundsare 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.

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