Bergman norm estimates of Poisson integrals (Q2725472)

In the half-space \({\mathbb R}^{n+1}_{+}\) it is known that a positive function can be in the harmonic Bergman space \(b^{p}\) only if \(p>1+1/n\). For a Poisson integral of \(f\) to be in \(b^{p}\) when \(1\leq p\leq 1+1/n\) it is therefore necessary that \(f\) satisfies some cancellation properties. In this paper these cancellation properties are explicitly described.