Estimates for integrals of derivatives of rational functions in multiply connected domains in the plane

2021/12/02 by Baranov, A. D., Kayumov, I. R.
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2112.01391

Abstract

We obtain estimates for integrals of derivatives of rational functions in multiply connected domains in the plane. A sharp order of the growth is found for the integral of the modulus of the derivative of a finite Blaschke product in the unit disk. We also extend the results of E.P. Dolzhenko about the integrals of the derivatives of rational functions to a wider class of domains, namely, to domains bounded by rectifiable curves without zero interior angles, and show the sharpness of the obtained results.

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