Remarks on a theorem by N. Yu. Antonov

• Autorzy: Per Sjölin , Fernando Soria
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 42B25: Maximal functions, Littlewood-Paley theory
• 42A20: Convergence and absolute convergence of Fourier and trigonometric series

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 158
• Numer: 1
• Strony: 79-97

Daty

wydano

2003

Twórcy

autor

Per Sjölin

• Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden

autor

Fernando Soria

• Department of Mathematics, C-XV, Universidad Autónoma de Madrid, E-28049 Madrid, Spain

Identyfikatory

DOI

10.4064/sm158-1-7