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An extremal property of outer functions

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Abstract

Our main result is the following: iff (z) is in the space H2, and F(z) is its outer part, then ‖F(n)‖H2≤‖‖F(n)‖H2(n=1,2,...), the left side being finite if the right side is finite. Under certain essential restrictions, this. inequality was proved by B. I. Korenblyum and V. S. Korolevich [1].

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Literature cited

  1. B. I. Korenblyum and V. S. Korolevich, “Regular functions analytic in a circle and smooth on its boundary,” Matem. Zametki,7, No. 2, 165–172 (1970).

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  2. K. Hoffman, Banach Spaces of Analytic Functions, Prentice-Hall, Englewood Cliffs, N.J. (1962).

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Authors and Affiliations

  1. Klev Structural-Engineering Institute, USSR

    B. I. Korenblyum

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  1. B. I. Korenblyum
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Translated from Matematicheskie Zametki, Vol. 10, No. 1, pp. 53–56, July, 1971.

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Korenblyum, B.I. An extremal property of outer functions. Mathematical Notes of the Academy of Sciences of the USSR 10, 456–458 (1971). https://doi.org/10.1007/BF01747069

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  • DOI: https://doi.org/10.1007/BF01747069

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