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Modulus of boundary values of analytic functions of class

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Abstract

Let ω be a modulus of continuity,

be the class of all functions analytic in the unit disk of the complex plane and such that

.

A condition is given (depending essentially on ω), necessary for a nonnegative function defined on the unit circle to coincide with the modulus of some function of class

.

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Literature cited

  1. N. A. Shirokov, Tr. Mat. Inst. Akad. Nauk,130, 196–222 (1978).

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Authors
  1. N. A. Shirokov
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 113, pp. 258–260, 1981.

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Shirokov, N.A. Modulus of boundary values of analytic functions of class . J Math Sci 22, 1870–1872 (1983). https://doi.org/10.1007/BF01882593

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  • DOI: https://doi.org/10.1007/BF01882593

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