Optimal estimates for harmonic functions in the unit ball

David Kalaj, Marijan Markovic

We find the sharp constants $C_p$ and the sharp functions $C_p=C_p(x)$ in the inequality $$|u(x)|\le \frac{C_p}{(1-|x{|}^2{)}^{(n-1)/p}}\Vert u{\Vert }_{h^p(B^n)},u\in h^p(B^n),x\in B^n,$$ in…