Cylindrical Carleman's formula of subharmonic functions and its application

Volume 11, Issue 8, pp 947--952 Publication Date: June 04, 2018       Article History


Lei Qiao - School of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou 450046, China.


Our aim in this paper is to prove the cylindrical Carleman's formula for subharmonic functions in a truncated cylinder. As an application, we prove that if the positive part of a harmonic function in a cylinder satisfies a slowly growing condition, then its negative part can also be dominated by a similar slowly growing condition, which improves some classical results about harmonic functions in a cylinder.