A weak-type inequality
of subharmonic functions
Abstract: We prove the weak-type inequality , , between a non-negative subharmonic function and an -valued smooth function , defined on an open set containing the closure of a bounded domain in a Euclidean space , satisfying , and , where is a constant. Here is the harmonic measure on with respect to 0. This inequality extends Burkholder's inequality in which and , a Euclidean space.
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- W. K. Hayman and P. B. Kennedy, Subharmonic functions, Academic, New York (1976). MR 57:665
- S. Lang, Analysis I, Addison-Wesley, Reading, Mass. (1968).
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Affiliation: Department of Mathematics, KAIST, Taejon 305-701, Korea
Keywords: Subharmonic function, smooth function, harmonic measure, weak-type inequality
Received by editor(s): May 9, 1996
Received by editor(s) in revised form: October 1, 1996
Additional Notes: This work was partially supported by GARC-KOSEF
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1998 American Mathematical Society