Øistein Søvik

Extremals for linear functionals on $H^p$ are outer when $0

Let $L$ be a nontrivial bounded linear functional on the Hardy space $H^p$ of the unit disc. We prove that if $0<p<1$ and if $f$ in the unit sphere of $H^p$ satisfies $L(f)=\|L\|$, then $f$ is an outer function. The proof is short and relies on a construction due to de Leeuw and Rudin. Our result complements work of Du...