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On the sharpness of the Stolz approach
Linköping University, The Institute of Technology. Linköping University, Department of Science and Technology, Communications and Transport Systems.ORCID iD: 0000-0002-3324-2298
Dipartimento di Scienze Universita G. dAnnunzio.
Department of Mathematics DePaul University.
Institute of Mathematics Akademia Podlaska.
2006 (English)In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 31, no 1, 47-59 p.Article in journal (Refereed) Published
Abstract [en]

We study the sharpness of the Stolz approach for the a.e. convergence of functions in the Hardy spaces in the unit disc, first settled in the rotation invariant case by J. E. Littlewood in 1927 and later examined, under less stringent, quantitative hypothesis, by H. Aikawa in 1991. We introduce a new regularity condition, of a qualitative type, under which we prove a version of Littlewood's theorem for tangential approach whose shape may vary from point to point. Our regularity condition can be extended in those contexts where no group is involved, such as NTA domains in Rn. We show exactly in what sense our regularity condition is sharp.

Place, publisher, year, edition, pages
2006. Vol. 31, no 1, 47-59 p.
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-35771Local ID: 28505OAI: oai:DiVA.org:liu-35771DiVA: diva2:256619
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2016-05-04

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http://www.math.helsinki.fi/Annales/Vol31/biase.html

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Svensson, Olof

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  • nn-NB
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