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.

Title

An-Najah University Journal for Research - Natural Sciences - Volume 16, Issue 2, 2002

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Publisher Country

Palestine

Publication Type

Both (Printed and Online)

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Year

2002

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