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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Conjugate Hardy's inequalities
with decreasing weights


Authors: Joan Cerdà and Joaquim Martín
Journal: Proc. Amer. Math. Soc. 126 (1998), 2341-2344
MSC (1991): Primary 42B25, 46E30
MathSciNet review: 1443375
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Abstract: We prove that for a decreasing weight $\omega$ on $ \mathbf{R}^+$, the conjugate Hardy transform is bounded on $L_p(\omega)$ ($1\leq p<\infty$) if and only if it is bounded on the cone of all decreasing functions of $L_p(\omega)$. This property does not depend on $p$.


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Additional Information

Joan Cerdà
Affiliation: Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, E-08071 Barcelona, Spain
Email: cerda@cerber.mat.ub.es

Joaquim Martín
Affiliation: Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, E-08071 Barcelona, Spain
Email: jmartin@cerber.mat.ub.es

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04273-7
PII: S 0002-9939(98)04273-7
Keywords: Conjugate Hardy's inequalities, decreasing weights
Received by editor(s): July 17, 1996
Received by editor(s) in revised form: January 16, 1997
Additional Notes: This work has been partially supported by DGICYT, Grant PB94-0879.
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1998 American Mathematical Society