On the restricted mean value property-Reference-Cited by-同舟云学术

On the restricted mean value property

Published:1987 Issue:3 Volume:100 Page:477-481
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Fenton P. C.

Abstract

Suppose that u u is continuous in the open unit disc and has the restricted mean value property. It is shown that if u u has finite boundary limits almost everywhere, and if u u possesses a harmonic majorant and minorant, the difference between which has finite radial upper limits everywhere, then u u is harmonic.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1987-100-03/S0002-9939-1987-0891149-1/S0002-9939-1987-0891149-1.pdf

Reference6 articles.

1. Functions having the restricted mean value property;Fenton, P. C.;J. London Math. Soc. (2),1976

2. A uniqueness theorem for a class of harmonic functions;Lohwater, A. J.;Proc. Amer. Math. Soc.,1952

3. The boundary values of a class of meromorphic functions;Lohwater, A. J.;Duke Math. J.,1952

4. S. Saks, Theory of the integral, PWN, Warsaw, 1937.

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