On interpolation in hardy-orlicz spaces

الملخص EN

The Hardy-Orlicz space Hφ is the space of all analytic functions f on the open unit disk D such that the subharmonic function φ(| f |) has a harmonic majorant on D , where φ is a modulus function.

H+φ is the subspace of Hφ consisting of all f φ ∈ H φ such that φ (| f |) has a quasi-bounded harmonic majorant on D.

If φ (x) = x p , 0 < p ≤ 1, then Hφ is the Hardy space Hp and if φ (x) = log(1+ x) , then Hφ is the Nevanlinna class N and H+φ is the Smirnov class N+ .

In this paper we generalize some of N.

Yanagihara's and A.

Hartmann's and others interpolation results from N and N+ to Hφ and H+φ.

For that purpose we generalize a canonical factorization theorem to functions in Hφ or + H+φ and introduce an F-space of complex sequences.

AMS subject Classification: Primary: 46Axx.Secondary: 46E10, 30H05