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Sharp weighted bounds for fractional integral operators |
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| Authors: | Michael T. Lacey Rodolfo H. Torres |
| Affiliation: | a Department of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA b Department of Mathematics, University of Kansas, 405 Snow Hall 1460 Jayhawk Blvd, Lawrence, KS 66045-7523, USA c Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, 41080 Sevilla, Spain |
| Abstract: | The 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. |
| Keywords: | Maximal operators Fractional integrals Singular integrals Weighted norm inequalities Extrapolation Sharp bounds |
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