Properties of local orthonormal systems, Part II: Geometric characterization of Bernstein inequalities

Jacek Gulgowski, Anna Kamont, Markus Passenbrunner

Let $(\hat{I}\text{c◯},\mathcal{F},\mathbb{P})$ be a probability space and let $({\mathcal{F}}_n)$ be a binary filtration, i.e. exactly one atom of ${\mathcal{F}}_{n-1}$ is divided into two atoms of $\…