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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.

- R Fefferman, R Gundy, M Silverstein, E M Stein
- Proceedings of the National Academy of Sciences…
- 1982

We show that the ratios (A(u)/N(u))(k)A(u) and (N(u)/A(u))(k)N(u) have L(p) norms equivalent with the H(p) norm of u. Here A(u) is the Lusin area integral and N(u) is the nontangential maximal function.

Article history: Received 9 May 2012 Received in revised form 9 July 2013 Accepted 27 July 2013 Available online 2 August 2013 Communicated by Richard Gundy

- V Dobri´c, R Gundy, P Hitczenko, Hernández Cohen, Weiss Wang, The
- 2001

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(R). Here, we treat the convergence problem by viewing the partial products as probabilities, converging weakly to… (More)

- Richard F. Gundy, Kazaros Kazarian
- SIAM J. Math. Analysis
- 2000

Article history: Received 22 April 2015 Accepted 6 October 2015 Available online 26 October 2015 Communicated by Richard Gundy

- Vladimir T. Dobric, Richard F. Gundy, Pawel Hitczenko
- SIAM J. Math. Analysis
- 2000

- MARCO ANNONI, LOUKAS GRAFAKOS, +4 authors P. A. Meyer
- 2009

The jth Rademacher function rj on [0, 1), j = 0, 1, 2, . . . , is defined as follows: r0 = 1, r1 = 1 on [0, 1/2) and r1 = −1 on [1/2, 1), r2 = 1 on [0, 1/4) ∪ [1/2, 3/4) and r2 = −1 on [1/4, 1/2) ∪ [3/4, 1), etc. The following is a classical result that can be found in Zygmund [10] (page 213): For every subset E of [0, 1] and every λ > 1, there is a… (More)

- R F GUNDY
- Journal of the experimental analysis of behavior
- 1959

- Gilles Pisier, Joachim Cuntz, Richard Gundy
- 2014

We describe a new operator space structure on Lp 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 operator… (More)