Zero sets of holomorphic functions in the unit ball with slow growth

Joaquim Bruna, Xavier Massaneda

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8 Citations (Scopus)

Abstract

We study the zero-varieties of holomorphic functions in the unit ball satisfying the growth condition log |f(z)|≤c fλ(|z|), where λ:(0,1)→ℝ+ is a positive increasing function. We obtain some sufficient conditions on an analytic variety to be defined by such a function. Some results for the particular case λ(r)=log(e/(1-r)), corresponding to the class A -∞, generalize those of B. Korenblum in one variable. © 1995 The Magnes Press, The Hebrew University.
Original languageEnglish
Pages (from-to)217-252
JournalJournal d'Analyse Mathématique
Volume66
DOIs
Publication statusPublished - 1 Dec 1995

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    Bruna, J., & Massaneda, X. (1995). Zero sets of holomorphic functions in the unit ball with slow growth. Journal d'Analyse Mathématique, 66, 217-252. https://doi.org/10.1007/BF02788823