The Constant of Interpolation in Bloch Type Spaces

Abstract

It is known that there exists a constant 0 < Δ1 < 1 such that any Δ1-separated sequence for the pseudohyperbolic distance in the open unit disk D of C is interpolating for the classical Bloch space B. We will prove that 0.8114 < Δ1 < 0.9785 and we will also generalize this result for Bloch type spaces Bvp for vp(z) = (1−|z| 2) p. In particular, we will provide a construction to calculate an estimate of the lower and upper bounds for the corresponding constant of separation Δp for these spaces. We also prove that Δp tends to 1 when p → ∞.