Geodesic
Remarks on a theorem by N. Yu. Antonov
Per Sjölin1 ; Fernando Soria2
1 Department of Mathematics Royal Institute of Technology S-100 44 Stockholm, Sweden
2 Department of Mathematics, C-XV Universidad Autónoma de Madrid E-28049 Madrid, Spain
Studia Mathematica, Tome 158 (2003) no. 1, pp. 79-97

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/sm158-1-7
Keywords: extend results antonov convergence fourier series general settings special feature work assume smoothness kernels hypotheses has interesting applications convergence respect general orthonormal systems walsh fourier system which prove convergence class mathop log nolimits mathop log nolimits mathop log nolimits mathop log nolimits other applications given theory differentiation integrals

Per Sjölin 1 ; Fernando Soria 2

1 Department of Mathematics Royal Institute of Technology S-100 44 Stockholm, Sweden
2 Department of Mathematics, C-XV Universidad Autónoma de Madrid E-28049 Madrid, Spain 
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Per Sjölin; Fernando Soria. Remarks on a theorem by N. Yu. Antonov. Studia Mathematica, Tome 158 (2003) no. 1, pp. 79-97. doi: 10.4064/sm158-1-7

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