Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Conjugate Hardy's inequalities with decreasing weights

Author(s): Joan Cerdà; 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 $p$ .

References:

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: 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
Copyright of article: Copyright 1998, American Mathematical Society

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