Positive Bilinear Mappings Associated with Stochastic Processes

Abstract

On some vector spaces of adapted stochastic processes, we define increasing families of positive bilinear forms, which generalize the usual square brackets [X,Y] and angle brackets ${\langle X,Y\rangle}$. We study the corresponding Hardy spaces especially for p = 1 or 2, and extend to this abstract framework results of Fefferman type from martingale theory.