Hokkaido Mathematical Journal

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

Riesz decomposition for superbiharmonic functions in the unit ball.

Hokkaido Mathematical Journal, 38 () pp.683-700

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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.

MSC(Primary)
MSC(Secondary)31B30(MSC2000), 31B05(MSC2000), 31B15(MSC2000)
Uncontrolled Keywordssuperbiharmonic functions; spherical means; Riesz decomposition;