On the restricted mean value property
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- by P. C. Fenton PDF
- Proc. Amer. Math. Soc. 100 (1987), 477-481 Request permission
Abstract:
Suppose that $u$ is continuous in the open unit disc and has the restricted mean value property. It is shown that if $u$ has finite boundary limits almost everywhere, and if $u$ possesses a harmonic majorant and minorant, the difference between which has finite radial upper limits everywhere, then $u$ is harmonic.References
- P. C. Fenton, Functions having the restricted mean value property, J. London Math. Soc. (2) 14 (1976), no. 3, 451–458. MR 437780, DOI 10.1112/jlms/s2-14.3.451
- John E. Littlewood, Some problems in real and complex analysis, D. C. Heath and Company Raytheon Education Company, Lexington, Mass., 1968. MR 0244463
- A. J. Lohwater, A uniqueness theorem for a class of harmonic functions, Proc. Amer. Math. Soc. 3 (1952), 278–279. MR 46494, DOI 10.1090/S0002-9939-1952-0046494-5
- A. J. Lohwater, The boundary values of a class of meromorphic functions, Duke Math. J. 19 (1952), 243–252. MR 48574 S. Saks, Theory of the integral, PWN, Warsaw, 1937. M. Tsuji, Potential theory in modern function theory, Chelsea, New York.
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 100 (1987), 477-481
- MSC: Primary 31A05
- DOI: https://doi.org/10.1090/S0002-9939-1987-0891149-1
- MathSciNet review: 891149