On Separated Carleson Sequences in the Unit Disc

The interpolating sequences S for H∞(D), the bounded holomorphic functions in the unit disc D of the complex plane C, were characterized by L. Carleson using metric conditions on S. Alternatively, to characterize interpolating sequences we can use the existence in H∞(D) of an infinity of functions {ρa}a∈S , uniformly bounded in D, the function ρa being 1 at the point a ∈ S and 0 at any b ∈ S \ {a}. A. Hartmann recently proved that just one function in H∞(D) was enough to characterize interpolating sequences for H∞(D). In this work we use the “hard” part of Carleson’s proof of the corona theorem to extend Hartmann’s result and to answer a question he asked in his paper. 2010 Mathematics Subject Classification: 30H10, 30H80.