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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A note on maximal inequalities


Author: Wo Sang Young
Journal: Proc. Amer. Math. Soc. 36 (1972), 207-211
MSC: Primary 28A20
DOI: https://doi.org/10.1090/S0002-9939-1972-0311866-0
MathSciNet review: 0311866
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Abstract: D. L. Burkholder and S. Sawyer extended in two apparently different directions a theorem of E. M. Stein involving maximal inequalities as necessary conditions for almost everywhere convergence. We will unify these theorems by showing that the like conclusions follow from certain conditions which are implied by each of Burkholder's and Sawyer's hypotheses.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0311866-0
Keywords: Maximal inequalities, sequences of operators, almost everywhere convergence
Article copyright: © Copyright 1972 American Mathematical Society