A Dirichlet norm inequality and some inequalities for reproducing kernel spaces
A Dirichlet norm inequality and some inequalities for reproducing kernel spaces
Let $f$ be analytic and of finite Dirichlet norm in the unit disk $\Delta$ with $f(0) = 0$. Then, for any $q > 0$, \[ \left \| {\exp f} \right \|_q^2 \leqslant \exp \left \{ {\frac {1} {{\pi q}}{{\int _\Delta {\left | {fâ(z)} \right |} }^2}d\sigma (z)} \right \}\quad (d\sigma …