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
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Bibliography
A. BAERNSTEIN II, Analytic functions of bounded mean oscillation, Durham Conference 1979.
N. DANIKAS, Untersuchungen über analytische Funktionen von beschränkter mittlerer Oszillation, Dissertation, Technische Universität Berlin 1981.
C. FEFFERMAN and E. STEIN, Hp spaces of several variables, Acta Math. 129 (1972), 137–193.
J. GARNETT, Bounded analytic functions, Academic Press 1981.
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
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