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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Boundedness of the fractional integral on
weighted Lebesgue and Lipschitz spaces


Authors: Eleonor Harboure, Oscar Salinas and Beatriz Viviani
Journal: Trans. Amer. Math. Soc. 349 (1997), 235-255
MSC (1991): Primary 42B25
MathSciNet review: 1357395
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9947-97-01644-9
PII: S 0002-9947(97)01644-9
Keywords: Fractional integral, weighted Lebesgue and Lipschitz spaces, weighted BMO
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.
Article copyright: © Copyright 1997 American Mathematical Society