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

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Harmonic Analysis

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

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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.

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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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Author information

Authors and Affiliations

  1. Kalavryton 37, Dasos Haidariou, Athens, Greece

    V. Nestoridis

  2. Athens University, Greece

    V. Nestoridis

  3. University of Crete, Greece

    V. Nestoridis

  4. Epidaurou 1, Chalandri, Athens, Greece

    N. Danikas

Authors
  1. V. Nestoridis
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  2. N. Danikas
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Editor information

Giancarlo Mauceri Fulvio Ricci Guido Weiss

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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

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