Hokkaido Mathematical Journal

Riesz decomposition for superbiharmonic functions in the unit ball

T. FUTAMURA, K. KITAURA, and Y. MIZUTA

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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

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1258554240

Digital Object Identifier
doi:10.14492/hokmj/1258554240

Mathematical Reviews number (MathSciNet)
MR2561956

Zentralblatt MATH identifier
1184.31009

Subjects
Primary: 31B30: Biharmonic and polyharmonic equations and functions
Secondary: 31B05: Harmonic, subharmonic, superharmonic functions 31B15: Potentials and capacities, extremal length

Keywords
superbiharmonic functions spherical means Riesz decomposition

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


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