Note on arc-length and harmonic measure
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- by John S. Spraker PDF
- Proc. Amer. Math. Soc. 105 (1989), 664-665 Request permission
Abstract:
In this note it is shown that the only Smirnov domain for which arc-length measure is harmonic measure is the disk. The proof depends on some facts about inner and outer functions and arc-length preserving maps.References
- Peter L. Duren, Theory of $H^{p}$ spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York-London, 1970. MR 0268655
- P. L. Duren, H. S. Shapiro, and A. L. Shields, Singular measures and domains not of Smirnov type, Duke Math. J. 33 (1966), 247β254. MR 199359 M. V. Keldysh and M. A. Lavrentiev, Sur la representation conforme des domains limites par des courbes rectifiables, Ann. Sci. Γcole Norm. Sup. 54 (1937), 1-38.
- George Piranian, Two monotonic, singular, uniformly almost smooth functions, Duke Math. J. 33 (1966), 255β262. MR 199320
Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 105 (1989), 664-665
- MSC: Primary 30C35; Secondary 30C85, 30D55, 31A15
- DOI: https://doi.org/10.1090/S0002-9939-1989-0956000-1
- MathSciNet review: 956000