Jointly maximal products in weighted growth spaces

2012/10/11 by Janne Gröhn, Gröhn, Janne, José Ángel Peláez +3 · 1 citation
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Primary 30J99 #math.CV #msc:30J99

paper · pdf · doi:10.48550/arxiv.1210.3318

arxiv created 2013/01/04 · arxiv updated 2013/01/07

Abstract

It is shown that for any non-decreasing, continuous and unbounded doubling function \om on [0,1), there exist two analytic infinite products f₀ and f₁ such that the asymptotic relation |f₀(z)| + |f₁(z)| \asymp \om(|z|) is satisfied for all z in the unit disc. It is also shown that both functions f_j for j=0,1 satisfy T(r,f_j)\asymplogω(r), as r→1^-, and hence give examples of analytic functions for which the Nevanlinna characteristic admits the regular slow growth induced by ω.

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• Embedding theorems for Bergman-Zygmund spaces induced by doubling weights

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