Probabilistic square functions and a priori estimates

Bennett, Andrew G.

doi:10.1090/S0002-9947-1985-0797052-2

Probabilistic square functions and a priori estimates
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Trans. Amer. Math. Soc. 291 (1985), 159-166 Request permission

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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Three variations on the theme of maximal functions