Isolated Singularities of Polyharmonic Inequalities

We study nonnegative classical solutions $u$ of the polyharmonic inequality $-{\mathrm{\Delta }}^{m}u>0$ in a punctured neighborhood of the origin in $R^n$. We give necessary and sufficient conditions on integers $n\ge 2$ and $m\ge 1$ such that these solutions $u$ satisfy a pointwise a priori bound as $x\to 0$.