Carleson measures for the area Nevanlinna spaces and applications

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Abstract

Let 1 < p < ∞ and let μ be a finite positive Borel measure on the unit disk D. The area Nevanlinna-Lebesgue space N p (μ) consists of all measurable functions h on D such that log+ |h| L p (μ), and the area Nevanlinna space N α p is the subspace consisting of all holomorphic functions, in N p ((1-|z|2)α dv(z)), where α > -1 and ν is area measure on D. We characterize Carleson measures for N α p , defined to be those measures μ for which N α p ⊂ N p (μ). As an application, we show that the spaces N α p are closed under both differentiation and integration. This is in contrast to the classical Nevanlinna space, defined by integration on circles centered at the origin, which is closed under neither. Applications to composition operators and to integral operators are also given.

Original languageEnglish
Pages (from-to)207-233
Number of pages27
JournalJournal d'Analyse Mathematique
Volume104
Issue number1
DOIs
Publication statusPublished - 2008 Jan

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)

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