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Properties of removable singularities for hardy spaces of analytic functions
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.ORCID iD: 0000-0002-9677-8321
2002 (English)In: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 66, no 3, 651-670 p.Article in journal (Refereed) Published
Abstract [en]

Removable singularities for Hardy spaces Hp(O) = {f ? Hol(O) :fp = u in O for some harmonic u}, 0 < p < 8 are studied. A set E ? O is a weakly removable singularity for Hp(O\E) if Hp(O\E) ? Hol(O), and a strongly removable singularity for Hp(O\E) if Hp(O\E) = Hp(O). The two types of singularities coincide for compact E, and weak removability is independent of the domain O. The paper looks at differences between weak and strong removability, the domain dependence of strong removability, and when removability is preserved under unions. In particular, a domain O and a set E ? O that is weakly removable for all Hp, but not strongly removable for any Hp(O\E), 0 < p < 8, are found. It is easy to show that if E is weakly removable for Hp(O\E) and q > p, then E is also weakly removable for Hq(O\E). It is shown that the corresponding implication for strong removability holds if and only if q/p is an integer. Finally, the theory of Hardy space capacities is extended, and a comparison is made with the similar situation for weighted Bergman spaces.

Place, publisher, year, edition, pages
2002. Vol. 66, no 3, 651-670 p.
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-46808DOI: 10.1112/S002461070200354XOAI: diva2:267704
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2013-12-17

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Björn, Anders
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