Function of $U$ -class and its applications.
Function of $U$ -class and its applications.
U$ -class.Let $w=f(z)$ be regular and $|f(z)|<1$ in $|z|<1$ , then by Fatou's theorem, $\lim_{z\rightarrow e^{i\theta}}f(z)=f(e^{i0})$ exists almost everywhere on $|z|=1$ , when $z\rightarrow e^{i\theta}$ from the inside of any Stolz domain, whose vertex is at $e^{i9}$ .If $|f(e^{t\theta})|=1$ almost everywhere, we say with $Seide1^{I)}$ that $f(z)$ belongs to U-class …