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Growth, Zero Distribution and Factorization of Analytic Functions of Moderate Growth in the Unit Disc

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Blaschke Products and Their Applications

Part of the book series: Fields Institute Communications ((FIC,volume 65))

Abstract

We give a survey of results on zero distribution and factorization of analytic functions in the unit disc in classes defined by the growth of log|f(re iθ)| in the uniform and integral metrics. We restrict ourself to the case of finite order of growth. For a Blaschke product B we obtain a necessary and sufficient condition for the uniform boundedness of all p-means of log|B(re iθ)|, where p>1.

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Acknowledgements

This paper was inspired by the “Conference on Blaschke Products and their Applications” (Fields Institute, Toronto, July 25–29, 2011) organized by Javad Mashreghi and Emmanuel Fricain. I would like to thank the organizers and the staff of the Fields Institute for hospitality and financial support.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Ivan Franko National University of Lviv, Universytets’ka 1, 79000, Lviv, Ukraine

    Igor Chyzhykov & Severyn Skaskiv

Authors
  1. Igor Chyzhykov
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  2. Severyn Skaskiv
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Corresponding author

Correspondence to Igor Chyzhykov .

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Editors and Affiliations

  1. , Département de mathématiques et de stati, Université Laval, avenue de la Médecine 1045, Quebec, G1K 7P4, Québec, Canada

    Javad Mashreghi

  2. , Institut Camille Jordan, Université Claude Bernard Lyon 1, avenue du 11 novembre 1918 43, Villeurbanne cedex, 69622, France

    Emmanuel Fricain

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Chyzhykov, I., Skaskiv, S. (2013). Growth, Zero Distribution and Factorization of Analytic Functions of Moderate Growth in the Unit Disc. In: Mashreghi, J., Fricain, E. (eds) Blaschke Products and Their Applications. Fields Institute Communications, vol 65. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-5341-3_8

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