liu.seSearch for publications in DiVA
Change search
ReferencesLink to record
Permanent link

Direct link
Removable singularities for weighted Bergman spaces
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-9677-8321
2006 (English)In: Czechoslovak Mathematical Journal, ISSN 0011-4642, Vol. 56, no 1, 179-227 p.Article in journal (Refereed) Published
Abstract [en]

We develop a theory of removable singularities for the weighted Bergman space. The general theory developed is in many ways similar to the theory of removable singularities for Hardy H p spaces, BMO and locally Lipschitz spaces of analytic functions, including the existence of counterexamples to many plausible properties, e.g. the union of two compact removable singularities needs not be removable. In the case when weak and strong removability are the same for all sets, in particular if μ is absolutely continuous with respect to the Lebesgue measure m, we are able to say more than in the general case. In this case we obtain a Dolzhenko type result saying that a countable union of compact removable singularities is removable. When dμ = wdm and w is a Muckenhoupt A p weight, 1 < p < ∞, the removable singularities are characterized as the null sets of the weighted Sobolev space capacity with respect to the dual exponent p′ = p/(p − 1) and the dual weight w′ = w 1/(1 − p).

Place, publisher, year, edition, pages
2006. Vol. 56, no 1, 179-227 p.
Keyword [en]
analytic continuation, analytic function, Bergman space, capacity, exceptional set, holomorphic function, Muckenhoupt weight, removable singularity, singular set, Sobolev space, weight
National Category
URN: urn:nbn:se:liu:diva-18240DOI: 10.1007/s10587-006-0012-xOAI: diva2:217142
The original publication is available at Anders Björn, Removable singularities for weighted Bergman spaces, 2006, Czechoslovak Mathematical Journal, (56), 1, 179-227. Copyright: Springer Science Business Media Available from: 2009-05-13 Created: 2009-05-13 Last updated: 2013-12-17Bibliographically approved

Open Access in DiVA

fulltext(454 kB)624 downloads
File information
File name FULLTEXT01.pdfFile size 454 kBChecksum SHA-512
Type fulltextMimetype application/pdf

Other links

Publisher's full text

Search in DiVA

By author/editor
Björn, Anders
By organisation
Applied MathematicsThe Institute of Technology
In the same journal
Czechoslovak Mathematical Journal

Search outside of DiVA

GoogleGoogle Scholar
Total: 624 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 999 hits
ReferencesLink to record
Permanent link

Direct link