Weighted Hardy spaces on the unit disk

Abstract

In this paper we mainly discuss three things. First, there is no canonical norm on the space $H_u^p(\mathbb{D})$. Second, we improve the weak-$\ast$ convergence of the measures ${\mu }_{u,r}$. Third, the dilations $f_t$ of the function $f\in H_u^p(\mathbb{D})$ converge to $f$ in $H_u^p$-norm and hence the polynomials are dense in $H_u^p(\mathbb{D})$.

11 pages. arXiv admin note: text overlap with arXiv:1309.6561

References in corpus (1)

• Poletsky-Stessin Hardy Spaces on Domains Bounded by An Analytic Jordan Curve in $\mathbb{C}$