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

Ariño, Miguel A.; Muckenhoupt, Benjamin

doi:10.1090/S0002-9947-1990-0989570-0

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
DOI: https://doi.org/10.1090/S0002-9947-1990-0989570-0
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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