Summability of Multi-Dimensional Fourier Series and Hardy Spaces

The history of martingale theory goes back to the early fifties when Doob [57] pointed out the connection between martingales and analytic functions. On the basis of Burkholder''s scientific achievements the mar­ tingale theory can perfectly well be applied in complex analysis and in the theory of classical Hardy spaces. This connection is the main point of Durrett''s book [60]. The martingale the...