Journal of Soviet Mathematics

, Volume 42, Issue 2, pp 1603–1610

Blaschke products satisfying the Carleson-Newman conditions and ideals of the algebra H

  • V. A. Tolokonnikov
Article

Abstract

One obtains tests for an ideal of the algebra H to contain a Blaschke product satisfying the Carleson-Newman condition. If the generalized divisor of the ideal is bounded on the space of maximal ideals of H, then the ideal contains a function with bounded divisor.

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Literature cited

  1. 1.
    B. I. Vasyunin, “Traces of bounded analytic functions on finite unions of Carleson sets,” J. Sov. Math.,27, No. 1 (1984).Google Scholar
  2. 2.
    T. W. Gamelin, Uniform Algebras, Prentice-Hall, Englewood Cliffs (1969).Google Scholar
  3. 3.
    J. B. Garnett, Bounded Analytic Functions, Academic Press, New York (1981).Google Scholar
  4. 4.
    N. K. Nikol'skii, Lectures on the Shift Operator [in Russian], Nauka, Moscow (1980).Google Scholar
  5. 5.
    V. A. Tolokonnikov, “Estimates in the Carleson corona theorem, ideals of the algebra H, a problem of Sz.-Nagy,” J. Sov. Math.,22, No. 6 (1983).Google Scholar
  6. 6.
    V. A. Tolokonnikov, “Interpolating Blaschke products and ideals of the algebra H,” J. Sov. Math.,27, No. 1 (1984).Google Scholar
  7. 7.
    K. Hoffman, “Bounded analytic functions and Gleason parts,” Ann. Math.,86, 74–111 (1967).Google Scholar
  8. 8.
    D. E. Marshall, Approximation and interpolation by inner functions. Thesis, Univ. of California, Los Angeles (1976).Google Scholar
  9. 9.
    M. Rosenblum, “A corona theorem for countably many functions,” Integral Equations Operator Theory,3, No. 1, 125–137 (1980).Google Scholar

Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • V. A. Tolokonnikov

There are no affiliations available

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