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

Joaquim Bruna, Xavier Massaneda

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Resum

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.
Idioma originalEnglish
Pàgines (de-a)217-252
RevistaJournal d'Analyse Mathématique
Volum66
DOIs
Estat de la publicacióPublicada - 1 de des. 1995

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