On homogeneous polynomials of several variables on the complex sphere

This article gives a generalization of a theorem of Ryll and Wojtaszczyk on the existence of a sequence of homogeneous polynomials $P_N$, $N=1,2,\dots$, in $d$ variables with degree $P_N=N$ for which
$$\|P_N\|_{L^2(S^d)}\geqslant c_d\|P_N\|_{C(S^d)}>0,$$
where $S^d$ is the sphere in $d$-dimensional complex space.
Bibliography: 11 titles.