Michael Lacey, Kabe Moen, Carlos Perez, Rodolfo H. Torres
Published 2009-05-23, updated 2010-02-02Version 2
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.
Comments: v2: changes made to reflect referee's report. Final version of the paper. To appear in J Func Anal
Journal: J. Funct. Anal. 259 (2010), no. 5, 1073-1097
Sharp weighted bounds involving A_\infty
Non-probabilistic proof of the A_2 theorem, and sharp weighted bounds for the q-variation of singular integrals
Two weight norm inequalities for fractional integral operators and commutators
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