The Constant of Interpolation in Bloch Type Spaces

Abstract

It is known that there exists a constant 0<Delta _1 < 1 such that any Delta _1-separated sequence for the pseudohyperbolic distance in the open unit disk textbf{D} of mathbb {C} is interpolating for the classical Bloch space mathcal {B}. We will prove that 0.8114< Delta _1 < 0.9785 and we will also generalize this result for Bloch type spaces mathcal {B}_{v_p} for v_p(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 Delta _p for these spaces. We also prove that Delta _p tends to 1 when p rightarrow infty .