Interpolation between Hardy spaces on the bidisc

Cesàro Summability of Two-Parameter Trigonometric-Fourier Series

“…) were proved in Fefferman, Stein [9], Gundy, Stein [12] and Lin [13]. Note that in case p=q the usual definition of Hardy spaces H p, p =H p and H > p, p =H > p are obtained.…”

Singular integrals on product domains

“…, k (k = d), this convergence result can also be found in Zhizhiashvili [16]. Moreover, by interpolation (see Lin [9] and Weisz [14]) we get from Theorem 1 and (1) that…”

The Maximal Riesz Operator of Two-Dimensional Fourier Transforms and Fourier Series on Hp(R×R) and Hp(T×T)

“…were proved in Fefferman and Stein [7], Gundy and Stein [11], and Lin [13]. Note that in case p=q the usual definition of Hardy spaces…”

“…Theorem 1 follows now from (12), (13), and Theorem B. K Note that for :=1 the proof is simpler because we do not need to estimate (A).…”

“…The following interpolation result concerning Hardy Lorentz spaces will be used several times in this paper (see Lin [13] and also Weisz [18]). …”