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Bi- subharmonic distributions on $$\mathbb{R}^ n$$ ($$n\geq 2$$). (Distributions bi-sousharmoniques sur $$\mathbb{R}^ n$$ ($$n\geq 2$$).) (French) Zbl 0802.31001
A locally summable function $$\omega$$ on $$\mathbb{R}^ n$$, $$n\geq 2$$, is said to be bi-subharmonic if $$\Delta^ 2 \omega\geq 0$$, where $$\Delta$$ is the Laplacian as a distribution. The author proves that a bi-subharmonic function is representable as a difference of two functions that are simultaneously bi-subharmonic and subharmonic if and only if $$\Delta\omega$$ coincides almost everywhere with a subharmonic function admitting a superharmonic minorant that is bounded above. There are also characterizations of biharmonic functions $$\omega$$ on $$\mathbb{R}^ 3$$ ($$\Delta^ 2 \omega=0$$) in terms of their averages over balls or spheres.
##### MSC:
 31B05 Harmonic, subharmonic, superharmonic functions in higher dimensions 31B30 Biharmonic and polyharmonic equations and functions in higher dimensions
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