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Interpolation and harmonic majorants in big Hardy-Orlicz spaces

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorHARTMANN, Andreas
dc.date.accessioned2024-04-04T03:16:24Z
dc.date.available2024-04-04T03:16:24Z
dc.date.created2006
dc.date.issued2007-12
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/194210
dc.description.abstractEnFree interpolation in Hardy spaces is characterized by the well-known Carleson condition. The result extends to Hardy-Orlicz spaces contained in the scale of classical Hardy spaces $H^p$, $p>0$. For the Smirnov and the Nevanlinna classes, interpolating sequences have been characterized in a recent paper in terms of the existence of harmonic majorants (quasi-bounded in the case of the Smirnov class). Since the Smirnov class can be regarded as the union over all Hardy-Orlicz spaces associated with a so-called strongly convex function, it is natural to ask how the condition changes from the Carleson condition in classical Hardy spaces to harmonic majorants in the Smirnov class. The aim of this paper is to narrow down this gap from the Smirnov class to ``big'' Hardy-Orlicz spaces. More precisely, we characterize interpolating sequences for a class of Hardy-Orlicz spaces that carry an algebraic structure and that are strictly bigger than $\bigcup_{p>0} H^p$. It turns out that the interpolating sequences are again characterized by the existence of quasi-bounded majorants, but now the functions defining these quasi-bounded majorants have to be in suitable Orlicz spaces. The existence of harmonic majorants defined by functions in such Orlicz spaces will also be discussed in the general situation. We finish the paper with a class of examples of separated Blaschke sequences that are interpolating for certain Hardy-Orlicz spaces without being interpolating for slightly smaller ones.
dc.language.isoen
dc.subject.enFree interpolation
dc.subject.enHardy-Orlicz spaces
dc.subject.enHarmonic majorants
dc.title.enInterpolation and harmonic majorants in big Hardy-Orlicz spaces
dc.typeArticle de revue
dc.identifier.doi10.1007/s11854-008-0006-8
dc.subject.halMathématiques [math]/Variables complexes [math.CV]
bordeaux.journalJournal d'Analyse Mathématiques
bordeaux.page197-219
bordeaux.volume103
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue3
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00125441
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00125441v1
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