Interpolating sequences in mean

This paper deals with interpolating sequences (z(n))(n) for two spaces of holomorphic functions f in the unit disk D in C: those that are bounded and those that satisfy a Lipschitz condition vertical bar f(z) - f(w)vertical bar <= c vertical bar z - w vertical bar(alpha), 0 < alpha <= 1. Given a sequence of values (w(n))(n) in a certain target space, we look for a function f interpolating 'in mean", that is, with (f(z(1)) + ... + f(z(n)))/n = w(n), n >= 1. We obtain target spaces when we prescribe that the corresponding interpolating sequences be the uniformly separated ones or the union of two uniformly separated ones. (C) 2018 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.