Best constants in the weak type inequalities for a martingale conditional square function (Q433566)

The author provides optimal-constant inequalities between the norms of a discrete-time Hilbert-valued martingale and both the norms of its square function and its conditional square function, respectively. The discrete-time set of the martingale is the set of the natural numbers, while the corresponding Hilbert space is separable. The sharpness of the corresponding constants is also examined, involving a sequence of independent Rademacher variables in both of the examples presented. The article is completed by references to the applications of the results, also involving sequences of independent Rademacher variables, to mathematical finance and areas of analysis.