Bellman functions and dimensionless estimates of Littlewood-Paley type
Dragičević, Oliver ; Volberg, Alexander
We use the Bellman function technique to obtain new Littlewood-Paley type estimates for classical as well as Gaussian spaces ▫$L^p({\mathbb{R}}^n)$▫. 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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