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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Maximal functions on classical Lorentz spaces and Hardy's inequality with weights for nonincreasing functions


Authors: Miguel A. Ariño and Benjamin Muckenhoupt
Journal: Trans. Amer. Math. Soc. 320 (1990), 727-735
MSC: Primary 42B25; Secondary 26D15, 46E30, 47B38
MathSciNet review: 989570
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Abstract: A characterization is given of a class of classical Lorentz spaces on which the Hardy Littlewood maximal operator is bounded. This is done by determining the weights for which Hardy's inequality holds for nonincreasing functions. An alternate characterization, valid for nondecreasing weights, is also derived.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1990-0989570-0
PII: S 0002-9947(1990)0989570-0
Article copyright: © Copyright 1990 American Mathematical Society