CHARACTERIZATIONS FOR THE FOCK-TYPE SPACES

We obtain Lipschitz type characterization and double integral characterization for Fock-type spaces with the norm parallel to f parallel to(Fm, alpha, tp)= integral(Cn )vertical bar f(z)e(-alpha vertical bar z vertical bar m)vertical bar(p )dV(z)/(1 + vertical bar z vertical bar)(t), where alpha > 0, t is an element of R and m is an element of N. The results of this paper are the extensions of the classical weighted Fock space F-2,alpha,t(p).