Note on potential theory for functions in Hardy classes

Details Note on potential theory for functions in Hardy classes Note on potential theory for functions in Hardy classes

2008-11-30

arxiv.org/abs/0812.0076v1

Mathematics

Complex Variables

3 pages

Scientific paper

The purpose of this note is to show that the set functions defined in \cite{trong-tuyen} can be suitably extended to all subsets $E$ of the unit disk $\mathbb{D}$. In particular we obtain uniform nearly-optimal estimates for the following quantity D_p(E,\epsilon, R) = \sup \{\sup_{|z| \leq R}|g(z)|: g\in H^p, ||g||_{H^p}\leq 1, (1-|\zeta |)|g(\zeta)| \leq \epsilon \forall \zeta\in E\}.

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