## Hokkaido Mathematical Journal

### Polysuperharmonic functions on a harmonic space

#### Abstract

In the context of the axiomatic potential theory, we introduce the notions of polyharmonic functions and polypotentials on a Brelot harmonic space $\Omega$. For these functions,we prove some results analogous to the Riesz decomposition, balayage, domination principle, etc., which are usually associated with harmonic and superharmonic functions on $\Omega$. We also consider the polyharmonic classifications of the harmonic spaces.

#### Article information

Source
Hokkaido Math. J., Volume 34, Number 2 (2005), 315-330.

Dates
First available in Project Euclid: 29 September 2010

https://projecteuclid.org/euclid.hokmj/1285766225

Digital Object Identifier
doi:10.14492/hokmj/1285766225

Mathematical Reviews number (MathSciNet)
MR2159000

Zentralblatt MATH identifier
1081.31008

Subjects
Primary: 31D05: Axiomatic potential theory
Secondary: 31B30: Biharmonic and polyharmonic equations and functions

#### Citation

AL-QURASHI, M.; ANANDAM, V. Polysuperharmonic functions on a harmonic space. Hokkaido Math. J. 34 (2005), no. 2, 315--330. doi:10.14492/hokmj/1285766225. https://projecteuclid.org/euclid.hokmj/1285766225