Boundedness of the fractional integral on weighted Lebesgue and Lipschitz spaces
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- by Eleonor Harboure, Oscar Salinas and Beatriz Viviani PDF
- Trans. Amer. Math. Soc. 349 (1997), 235-255 Request permission
Abstract:
Necessary and sufficient conditions are given for the fractional integral operator $I_\alpha$ to be bounded from weighted strong and weak $L^p$ spaces within the range $p\geq n/\alpha$ into suitable weighted $BMO$ and Lipschitz spaces. We also characterize the weights for which $I_\alpha$ can be extended to a bounded operator from weighted $BMO$ into a weighted Lipschitz space of order $\alpha$. Finally, under an additional assumption on the weight, we obtain necessary and sufficient conditions for the boundedness of $I_\alpha$ between weighted Lipschitz spaces.References
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Additional Information
- Eleonor Harboure
- Affiliation: Programa Especial de Matemática Aplicada and Facultad de Ingenier ía Qu í mica, Universidad Nacional del Litoral, Güemes 3450, 3000 Santa Fe, Rep. Argentina
- Oscar Salinas
- Affiliation: Programa Especial de Matemática Aplicada and Facultad de Ingenier ía Qu í mica, Universidad Nacional del Litoral, Güemes 3450, 3000 Santa Fe, Rep. Argentina
- Beatriz Viviani
- Affiliation: Programa Especial de Matemática Aplicada and Facultad de Ingenier ía Qu í mica, Universidad Nacional del Litoral, Güemes 3450, 3000 Santa Fe, Rep. Argentina
- Received by editor(s): June 26, 1995
- Additional Notes: The authors were supported by the Consejo Nacional de Investigaciones Cient íficas y Técnicas de la República Argentina and by the Universidad Nacional del Litoral, CAI+D Program.
- © Copyright 1997 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 349 (1997), 235-255
- MSC (1991): Primary 42B25
- DOI: https://doi.org/10.1090/S0002-9947-97-01644-9
- MathSciNet review: 1357395