On the sharpness of the Stolz approach
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
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.
Engineering and Technology
IdentifiersURN: urn:nbn:se:liu:diva-35771Local ID: 28505OAI: oai:DiVA.org:liu-35771DiVA: diva2:256619