Upper bounds for the \(L_ p\)-norms of martingales
Let \((f_ n)\) be a martingale. We establish a relationship between exponential bounds for the probabilities of the type \(P(| f_ n| >\lambda \cdot \| T(f_ n)\|_{\infty})\) and the size of the constant \(C_ p\) appearing in the inequality \(\| f^*\|_ p\leq C_ p\| T^*(f)\|_ p\), for some quasi-linear operators acting on martingales.
scientific article; zbMATH DE number 4109725
scientific article