H-infinity space
= H-infinity space
{c}
{title2=$H^\infty(\mathbb D)$}
This <Hardy space> consists of bounded <holomorphic functions> on the <unit disc>, with norm $\|f\|_\infty=\sup_{z\in\mathbb D}|f(z)|$. Its almost-everywhere boundary realization follows from the <Fatou theorem for bounded holomorphic functions>.