SOME CONSEQUENCES OF PISIER APPROACH TO INTERPOLATION

A recent result of Pisier on K-functionals is exploited in the context of function spaces defined from singular integrals. The main consequences appear for H(P) spaces on the complex ball (1 < p less-than-or-equal-to infinity) and spaces of differentiable functions in several variables. It turns out that the complex variable arguments used in [PI] may in certain cases be substituted for real variable methods, which of course have a wider range of applicability. We discuss interpolation of vector valued Hardy spaces on the ball and prove that L1(S)/H-1(B) satisfies Grothendieck's theorem, similarly as in the disc case.