Interpolating sequences in mean

This paper deals with interpolating sequences (zn)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 |f(z)−f(w)|≤c|z−w|α, 0<α≤1. Given a sequence of values (wn)n in a certain target space, we look for a function f interpolating 'in mean”, that is, with (f(z1)+⋯+f(zn))∕n=wn, 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.