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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Probabilistic square functions and a priori estimates

Author: Andrew G. Bennett
Journal: Trans. Amer. Math. Soc. 291 (1985), 159-166
MSC: Primary 42B20; Secondary 42A61, 42B25, 60J65
MathSciNet review: 797052
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Abstract: We obtain a priori estimates for Riesz transforms and their variants, that is, estimates with bounds independent of the dimension of the space and/or the nature of the boundary. The key to our results is to give probabilistic definitions which do not depend on the geometry of the situation for the transformations in question. We then use probabilistic square functions to prove our a priori estimates.

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Article copyright: © Copyright 1985 American Mathematical Society

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