On Homogeneous Polynomials on a Complex Ball

We prove that there exist -homogeneous polynomials on a complex -dimensional ball such that <!-- MATH ${\left\| {{p_n}} \right\|_\infty} = 1$ --> and <!-- MATH ${\left\| {{p_n}} \right\|_2} \geqslant \sqrt \pi {2^{- d}}$ --> . This enables us to answer some questions about and Bloch spaces on a complex ball. We also investigate interpolation by -homogeneous polynomials on a -dimensional complex ball.