Support points of the unit ball of $H^{p}$ $(1\leq p\leq \infty )$

Abstract:

The following results are obtained for the ${H^p}$ class, over the open unit disc, whenever $1 \leqslant p \leqslant \infty$. (1) $f$ is a support point of the unit ball of ${H^p}$, whenever $1 \leqslant p < \infty$, if and only if ${|| f ||_p} = 1$ and $f$ is of the form $f(z) = {[Q(z)]^{2/p}} \cdot W(z)$ where $W(z)$ is a function analytic in the closed unit disc and nonvanishing on its boundary and $Q(z)$ is either a nonzero constant or a polynomial with all of its zeros on the boundary of the unit disc. (2) $f$ is a support point of the unit ball of ${H^\infty }$ if and only if $f$ is a finite Blaschke product.