Hiroshima Mathematical Journal

Isolated singularities, growth of spherical means and Riesz decomposition for superbiharmonic functions

Toshihide Futamura, Keiji Kitaura, and Yoshihiro Mizuta

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Abstract

We consider Riesz decomposition theorem for superbiharmonic functions in the punctured ball. In fact, we show that under certain growth condition on surface integrals, superbiharmonic functions are represented as a sum of potentials and biharmonic functions.

Article information

Source
Hiroshima Math. J., Volume 38, Number 2 (2008), 231-241.

Dates
First available in Project Euclid: 5 September 2008

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1220619459

Digital Object Identifier
doi:10.32917/hmj/1220619459

Mathematical Reviews number (MathSciNet)
MR2437573

Zentralblatt MATH identifier
1161.31302

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

Keywords
superbiharmonic functions spherical means Riesz decomposition

Citation

Futamura, Toshihide; Kitaura, Keiji; Mizuta, Yoshihiro. Isolated singularities, growth of spherical means and Riesz decomposition for superbiharmonic functions. Hiroshima Math. J. 38 (2008), no. 2, 231--241. doi:10.32917/hmj/1220619459. https://projecteuclid.org/euclid.hmj/1220619459


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