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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Elementary reverse Hölder type
inequalities with application to
operator interpolation theory


Authors: Jesús Bastero and Francisco J. Ruiz
Journal: Proc. Amer. Math. Soc. 124 (1996), 3183-3192
MSC (1991): Primary 46E30, 46B70
DOI: https://doi.org/10.1090/S0002-9939-96-03651-9
MathSciNet review: 1363446
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Abstract: We give a very elementary proof of the reverse Hölder type inequality for the classes of weights which characterize the boundedness on $L^{p}$ of the Hardy operator for nonincreasing functions. The same technique is applied to Calderón operator involved in the theory of interpolation for general Lorentz spaces. This allows us to obtain further consequences for intermediate interpolation spaces.


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Additional Information

Jesús Bastero
Affiliation: Department of Mathematics, University of Zaragoza, 50009-Zaragoza, Spain
Email: bastero@posta.unizar.es

Francisco J. Ruiz
Affiliation: Department of Mathematics, University of Zaragoza, 50009-Zaragoza, Spain
Email: fjruiz@posta.unizar.es

DOI: https://doi.org/10.1090/S0002-9939-96-03651-9
Keywords: Hardy operator, weighted norm inequalities, Lorentz spaces, interpolation of operators
Received by editor(s): May 22, 1993
Received by editor(s) in revised form: April 10, 1995
Additional Notes: The first author was partially supported by DGICYT PS90-0120
The second author was partially supported by DGICYT PS89-0181 and DGICYT PS93-0228-C02-02.
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1996 American Mathematical Society