JEDNOSTKA NAUKOWA KATEGORII A+

# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Remarks on a theorem by N. Yu. Antonov

### Tom 158 / 2003

Studia Mathematica 158 (2003), 79-97 MSC: 42A20, 42B25. DOI: 10.4064/sm158-1-7

#### Streszczenie

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 $L\mathop {\rm log}\nolimits L \mathop {\rm log}\nolimits \mathop {\rm log}\nolimits \mathop {\rm log}\nolimits L$. Other applications are given in the theory of differentiation of integrals.

#### Autorzy

• Per SjölinDepartment of Mathematics
Royal Institute of Technology
S-100 44 Stockholm, Sweden
e-mail
• Fernando SoriaDepartment of Mathematics, C-XV