Properties of Removable Singularities for Hardy Spaces of Analytic Functions |
| |
Authors: | Bjorn Anders |
| |
Affiliation: | Department of Mathematics, Linköping University SE-581 83 Linköping, Sweden, anbjo{at}mai.liu.se |
| |
Abstract: | Removable singularities for Hardy spaces Hp() = {f Hol(): |f|p u in for some harmonic u}, 0 < p < are studied. A setE = is a weakly removable singularity for Hp(E) if Hp(E) Hol(), and a strongly removable singularity for Hp(E) if Hp(E)= Hp(). The two types of singularities coincide for compactE, and weak removability is independent of the domain . The paper looks at differences between weak and strong removability,the domain dependence of strong removability, and when removabilityis preserved under unions. In particular, a domain and a setE that is weakly removable for all Hp, but not strongly removablefor any Hp(E), 0 < p < , are found. It is easy to show that if E is weakly removable for Hp(E)and q > p, then E is also weakly removable for Hq(E). Itis shown that the corresponding implication for strong removabilityholds if and only if q/p is an integer. Finally, the theory of Hardy space capacities is extended, anda comparison is made with the similar situation for weightedBergman spaces. |
| |
Keywords: | |
本文献已被 Oxford 等数据库收录! |
|