Martingale Hardy spaces, BMO and VMO spaces with nonlinearly ordered stochastic basis (Q920475)

Some duality results of martingale theory are generalized in the case when the stochastic basis is nonlinearly ordered. The concepts of \(\infty\)-atom and atomic Hardy space are introduced. Duality between atomic Hardy, BMO and VMO spaces are proved. The analogue of the classical Hardy inequality is given for Walsh-Fourier coefficients of functions belonging to the two-dimensional dyadic Hardy space. Some of these theorems are generalized for q-atoms in another paper of the author titled ``Atomic Hardy spaces'' (to appear in the same journal).