## Hokkaido Mathematical Journal

### Riesz decomposition for superbiharmonic functions in the unit ball

#### Abstract

For a superbiharmonic function $u$ in the unit ball with the growth condition of spherical means, we show that $u$ is represented as the sum of a generalized Riesz potential and a biharmonic function. This representation is referred to as Riesz decomposition for superbiharmonic functions. \\ ~~~The superharmonic case is treated similarly.

#### Article information

Source
Hokkaido Math. J., Volume 38, Number 4 (2009), 683-700.

Dates
First available in Project Euclid: 18 November 2009

https://projecteuclid.org/euclid.hokmj/1258554240

Digital Object Identifier
doi:10.14492/hokmj/1258554240

Mathematical Reviews number (MathSciNet)
MR2561956

Zentralblatt MATH identifier
1184.31009

#### Citation

FUTAMURA, T.; KITAURA, K.; MIZUTA, Y. Riesz decomposition for superbiharmonic functions in the unit ball. Hokkaido Math. J. 38 (2009), no. 4, 683--700. doi:10.14492/hokmj/1258554240. https://projecteuclid.org/euclid.hokmj/1258554240