On L¹-estimates of derivatives of univalent rational functions

2013/12/11 by Baranov, Anton D., Fedorovskiy, Konstantin Yu.
#30C20 #30E10 #30J10 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1312.3312

Abstract

We study the growth of the quantity ∫_\mathbbT|R'(z)| dm(z) for rational functions R of degree n, which are bounded and univalent in the unit disk, and prove that this quantity may grow as n^γ, γ>0, when n→∞. Some applications of this result to problems of regularity of boundaries of Nevanlinna domains are considered. We also discuss a related result by Dolzhenko which applies to general (non-univalent) rational functions.

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