On p-harmonic measures in half-spaces

For all $$10$$ such that the p-harmonic measure in $${\mathbb {R}}^N_+$$ of a ball of radius $$0 < \delta \le 1$$ in $${\mathbb {R}}^{N-1}$$ is bounded above and below by a constant times $$\delta ^{\alpha (p.N)}$$ . We provide explicit estimates for the exponent $$\alpha (p,N)$$ .