Remarks on a theorem by N. Yu. Antonov
2003 (English)In: Studia Mathematica, ISSN 0039-3223, Vol. 158, no 1, 79-97 p.Article in journal (Refereed) Published
We extend some results of N. Yu. Antonov on convergence of Fourier series to more general settings. One special feature of our work is that we do not assume smoothness for the kernels in our hypotheses. This has interesting applications to convergence with respect to general orthonormal systems, like the Walsh-Fourier system, for which we prove a.e. convergence in the class L log L log log log L. Other applications are given in the theory of differentiation of integrals.
Place, publisher, year, edition, pages
2003. Vol. 158, no 1, 79-97 p.
fourier-series, convergence, integrals, ae
IdentifiersURN: urn:nbn:se:kth:diva-22944ISI: 000186451500007OAI: oai:DiVA.org:kth-22944DiVA: diva2:341642
QC 201005252010-08-102010-08-10Bibliographically approved