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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
DOI: https://doi.org/10.1090/S0002-9939-98-04273-7
MathSciNet review: 1443375
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Abstract | References | Similar Articles | Additional Information

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 $p$.


References [Enhancements On Off] (What's this?)

  • 1. M. Ariño and B. Muckenhoupt, Maximal functions on classical Lorentz spaces and Hardy's inequality with weights for nonincreasing functions, Trans. Amer. Math. Soc. 320(1990), 727-735 MR 90k:42034
  • 2. B. Muckenhoupt, Hardy's inequality with weights, Studia Math. 44(1972), 31-38 MR 47:418
  • 3. C.J. Neugebauer, Some classical operators on Lorentz space, Forum Math. 4(1992), 135-146. MR 93i:42013

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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: https://doi.org/10.1090/S0002-9939-98-04273-7
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

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