Multi-Dimensional Dyadic Hardy Spaces

The theory of the one-dimensional classical Hardy spaces are described in the books Duren [59], Stein [193, 194], Stein and Weiss [192], Lu [125] and Uchiyama [205] in details (see also Fefferman and Stein [67]). Motivated by the works of Burkholder, Davis and Gundy [21, 20, 52], the one-dimensional martingale Hardy spaces are investigated in Garsia [83], Neveu [138], Dellacherie and Meyer [54, 55], Long [124] and Weisz [216]. With the help of the Brownian motion one can find a strong connection between these two types of Hardy spaces (see Durrett [60] and Bass [4]).