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
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by Miguel A. Ariño and Benjamin Muckenhoupt PDF

Trans. Amer. Math. Soc. 320 (1990), 727-735 Request permission

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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