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Removable singularities for H-p spaces of analytic functions, 0 < p < 1
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.ORCID iD: 0000-0002-9677-8321
2001 (English)In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, Vol. 26, no 1, 155-174 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we study removable singularities for Hardy H-p spaces of analytic functions on general domains, mainly for 0 < p < 1. For each p < 1 we prove that there is a self-similar linear Canter set with Hausdorff dimension greater than 0.4p removable for H-p, thereby obtaining the first removable sets with positive Hausdorff dimension for 0 < p < 1. (Cf. the author's older result that a set E removable for H-P, 0 < p < 1, must satisfy dim E p.) We use this to extend some results earlier proved for 1 less than or equal to p < to 0 < p < infinity or 1/2 less than or equal to p < .

Place, publisher, year, edition, pages
2001. Vol. 26, no 1, 155-174 p.
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-49327OAI: diva2:270223
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2013-12-17

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