On orthogonally scattered dilations of bounded vector measures

L-orthogonally scattered measures

Vector Valued Measures of Bounded Mean Oscillation

The duality between Hl and BMO, the space of functions of bounded mean oscillation (see [JN]), was first proved by C. Fefferman (see [F], [FS]) and then other proofs of it were obtained . Using the atomic decomposition approach ([C], [L]) the author studied the problem of characterizing the dual space of Hl of vector-valued functions . In [B2] the author showed, for the case SZ = {Iz1 = 1}, tha...

Vector measures of bounded γ-variation and stochastic integrals

Here, the driving process B is a (semi)martingale (for instance, a Brownian motion), and φ is a stochastic process satisfying suitable measurability and integrability conditions. This observation has been used by various authors as the starting point of a theory of stochastic integration for vector-valued processes. Let X be a Banach space. In [5] we characterized the class of functions φ : (0,...

On the Existence of a Control Measure for Strongly Bounded Vector Measures

In this note we extend a theorem of Bartle, Dunford, and Schwartz [ l ] which states that for every countably additive measure denned on a (T-algebra there exists a positive "control measure" v such that v{E)—>0 if and only if ||/z||(.E) —»0, where ||/x|| is the semivariation of JJL. In this paper, ju, which is defined on a ring S, is assumed to be finitely additive and strongly bounded (^-boun...

On Vector Functions of Bounded Convexity

Let X be a normed linear space. We investigate properties of vector functions F : [a, b] → X of bounded convexity. In particular, we prove that such functions coincide with the delta-convex mappings admitting a Lipschitz control function, and that convexity K aF is equal to the variation of F ′ + on [a, b). As an application, we give a simple alternative proof of an unpublished result of the fi...