Geodesic
Application of Conformal Mappings to Inequalities for Trigonometric Polynomials
Matematičeskie zametki, Tome 76 (2004) no. 3, pp. 396-408

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In this paper, we obtain inequalities for trigonometric and algebraic polynomials supplementing and strengthening the classical results going back to papers of S. N. Bernstein and I. I. Privalov. The method of proof is based on the construction of the conformal and univalent mapping from a given trigonometric polynomial and on the application of results of the geometric theory of functions of a complex variable to this mapping. 
@article{MZM_2004_76_3_a8,
     author = {A. V. Olesov},
     title = {Application of {Conformal} {Mappings} to {Inequalities} for {Trigonometric} {Polynomials}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {396--408},
     publisher = {mathdoc},
     volume = {76},
     number = {3},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_76_3_a8/}
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A. V. Olesov. Application of Conformal Mappings to Inequalities for Trigonometric Polynomials. Matematičeskie zametki, Tome 76 (2004) no. 3, pp. 396-408. http://geodesic.mathdoc.fr/item/MZM_2004_76_3_a8/