Richard F. Gundy

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We show that the H(p) spaces on the bi-disc can be characterized in terms of either the nontangential maximal function and the area integral or their probabilistic analogues resulting by introducing two-time Brownian motion (i.e., the martingale maximal function) and the corresponding square function.
of probabilities. Abstract. The construction of a multiresolution analysis starts with the specification of a scale function. The Fourier transform of this function is defined by an infinite product. The convergence of this product is usually discussed in the context of L 2 (R). Here, we treat the convergence problem by viewing the partial products as(More)
We describe a new operator space structure on L p when p is an even integer and compare it with the one introduced in our previous work using complex interpolation. For the new structure, the Khintchine inequalities and Burkholder's martingale inequalities have a very natural form: the span of the Rademacher functions is completely isomorphic to the(More)