Note on potential theory for functions in Hardy classes
arXiv:0812.0076
Abstract
The purpose of this note is to show that the set functions defined in \cite{trong-tuyen} can be suitably extended to all subsets of the unit disk . In particular we obtain uniform nearly-optimal estimates for the following quantity D_p(E,ε, R) = \sup \{\sup_{|z| \leq R}|g(z)|: g\in H^p, ||g||_{H^p}\leq 1, (1-|ζ|)|g(ζ)| \leq ε\forall ζ\in E\}.
3 pages