Extremals for linear functionals on $H^p$ are outer when $0<p<1$

Ole Fredrik Brevig, Øistein Søvik

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 $L(f)=\Vert L\Vert$,…