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Interval averages of H1-functions and BMO norm of inner functions

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Part of the Lecture Notes in Mathematics book series (LNM,volume 992)

Abstract

The main result of this paper states that every value of an Hi-function taken at an interior point is equal to the average of the function on a boundary interval. This fact is used in order to find the exact value of the BMO norm of inner functions.

Keywords

  • Holomorphic Function
  • Conformal Mapping
  • Blaschke Product
  • Boundary Interval
  • Open Unit Disc

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bibliography

  1. A. BAERNSTEIN II, Analytic functions of bounded mean oscillation, Durham Conference 1979.

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  2. N. DANIKAS, Untersuchungen über analytische Funktionen von beschränkter mittlerer Oszillation, Dissertation, Technische Universität Berlin 1981.

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  3. C. FEFFERMAN and E. STEIN, Hp spaces of several variables, Acta Math. 129 (1972), 137–193.

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  4. J. GARNETT, Bounded analytic functions, Academic Press 1981.

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  5. W. RUDIN, Function theory in the unit ball of ℂn, Springer Verlag

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© 1983 Springer-Verlag

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Nestoridis, V., Danikas, N. (1983). Interval averages of H1-functions and BMO norm of inner functions. In: Mauceri, G., Ricci, F., Weiss, G. (eds) Harmonic Analysis. Lecture Notes in Mathematics, vol 992. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069158

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  • DOI: https://doi.org/10.1007/BFb0069158

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12299-9

  • Online ISBN: 978-3-540-39885-1

  • eBook Packages: Springer Book Archive