Martingale Orlicz-Hardy spaces for continuous-time (Q6548000)

The authors introduce several martingale Orlicz-Hardy spaces with continuous time. Historically, the research on discrete-time martingale Hardy spaces and their variants has yielded fruitful results. However, compared with discrete-time martingales, Hardy spaces of continuous-time martingales are rarely studied (some references are given in the paper). In the present paper, the authors follow the approach of the paper of \textit{F. Weisz} [in: Probability theory and applications. Essays to the memory of József Mogyoródi. Dordrecht: Kluwer Academic Publishers. 47--75 (1992; Zbl 0851.60043)], and consider the martingale Orlicz-Hardy spaces with continuous-time, which are respectively defined via maximal function, quadratic variation, conditional quadratic variation and predictable majorant. The authors give the atomic characterization in the form of atomic decomposition theorem for these spaces and, as applications, obtain some martingale inequalities and the duality result, receiving the generalized martingale Campanato space as the dual space.