Geodesic
Estimates for the
Izvestiya. Mathematics , Tome 86 (2022) no. 5, pp. 839-851

Voir la notice de l'article provenant de la source Math-Net.Ru

We obtain estimates for the integrals of derivatives of rational functions in multiply connected domains in the plane. A sharp order of growth is found for the integral of the modulus of the derivative of a finite Blaschke product in the unit disc. We also extend the results of 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 results obtained.
Keywords: rational function, Blaschke product, Hardy space
Mots-clés : conformal map, John domain. 
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     author = {A. D. Baranov and I. R. Kayumov},
     title = {Estimates for the},
     journal = {Izvestiya. Mathematics },
     pages = {839--851},
     publisher = {mathdoc},
     volume = {86},
     number = {5},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2022_86_5_a1/}
}
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A. D. Baranov; I. R. Kayumov. Estimates for the. Izvestiya. Mathematics , Tome 86 (2022) no. 5, pp. 839-851. http://geodesic.mathdoc.fr/item/IM2_2022_86_5_a1/