Journal of Operator Theory

Volume 56, Issue 1, Summer 2006 pp. 167-198.

Bellman functions and dimensionless estimates of Littlewood-Paley type

Authors: Oliver Dragi\v{c}evi\'c (1) and Alexander Volberg (2)
Author institution: (1) Department of Mathematics, Michigan State University, East Lansing, MI 48823, USA and Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Slovenia
(2) Department of Mathematics, Michigan State University, East Lansing, MI 48823, USA

Summary: We use the Bellman function technique to obtain new Littlewood-Paley type estimates for classical as well as Gaussian spaces $L^p(\R^n)$. This is our principal result. The rest of the paper is purely methodological: it contains unified proofs of the known results. Namely, we present the uniform approach to proofs of the existence of dimension free bounds for corresponding Riesz transforms. Some of our results contain best to-date constants.

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