Hardy space interpolation in the unit ball

Interpolating sequences for the spaces H^p(Bⁿ), 1 <-p < ∞, n≥2, are studied. In contrast to the case n = 1, they are not the same for all p, but Varopoulos' necessary condition for H^∞ interpolation turns out to be necessary for H^p interpolation, for any p≥ 1, and sufficient for the sequence to be a finite union of H¹ interpolating sequences. Sufficient conditions are given for H^p interpolation, npn/(n-1), which are intermediary between Varopoulos' condition and Berndtsson's sufficient condition for H^∞(Bⁿ) interpolation.