An extension of Krzyżʹs conjecture

For α∈(0 1) the problem of finding sup|fn|f for holomorphic functions f(z)=f0+f1z+⋯ in the unit disk |z|<1 with α<|f(z)|<1 is discussed and an extension of Krzyżʹs conjecture is given. The Landau problem in every such class is also discussed.