Spherical means and Riesz decomposition for superbiharmonic functions (Q2497091)

A locally integrable function \(u\) in \(\Omega \subset \) \(\mathbb{R}^{n}\) is called superbiharmonic in \(\Omega \) if \(\triangle ^{2}u\) in the distributional sense is a nonnegative measure on \(\Omega \). Denoting a spherical mean with respect to the ball \(B(0,r) \) by \(M(r,u) \), \textit{Premalatha} [Arab. J. Math. Sci. 7, No. 1, 47--52 (2001; Zbl 0986.31001)] proved that \(M(r^2,u)- M(r,u)\) is bounded for superharmonic functions when \(r>1\). The authors extend this result for superbiharmonic functions.