Conjugate Hardy’s inequalities with decreasing weights
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- by Joan Cerdà and Joaquim Martín PDF
- Proc. Amer. Math. Soc. 126 (1998), 2341-2344 Request permission
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
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- Benjamin Muckenhoupt, Hardy’s inequality with weights, Studia Math. 44 (1972), 31–38. MR 311856, DOI 10.4064/sm-44-1-31-38
- C. J. Neugebauer, Some classical operators on Lorentz space, Forum Math. 4 (1992), no. 2, 135–146. MR 1155311, DOI 10.1515/form.1992.4.135
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
- 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
- © Copyright 1998 American Mathematical Society
- 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