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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A weighted weak type inequality for the maximal function


Author: E. Sawyer
Journal: Proc. Amer. Math. Soc. 93 (1985), 610-614
MSC: Primary 42B25
MathSciNet review: 776188
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Abstract: We show that the operator $ S = {\upsilon ^{ - 1}}M\upsilon $, where $ M$ denotes the HardyLittlewood maximal operator, is of weak type (1,1) with respect to the measure $ \upsilon (x)w(x)dx$ whenever $ \upsilon $ and $ w$ are $ {A_1}$ weights. B. Muckenhoupt's weighted norm inequality for the maximal function can then be obtained directly from the P. Jones factorization of $ {A_p}$ weights using interpolation with change of measure.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0776188-1
PII: S 0002-9939(1985)0776188-1
Article copyright: © Copyright 1985 American Mathematical Society