Remarks on a theorem by N. Yu. Antonov

Per Sjölin, and Fernando Soria. "Remarks on a theorem by N. Yu. Antonov." Studia Mathematica 158.1 (2003): 79-97. <http://eudml.org/doc/284431>.

@article{PerSjölin2003,
abstract = {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.},
author = {Per Sjölin, Fernando Soria},
journal = {Studia Mathematica},
language = {eng},
number = {1},
pages = {79-97},
title = {Remarks on a theorem by N. Yu. Antonov},
url = {http://eudml.org/doc/284431},
volume = {158},
year = {2003},
}

TY - JOUR
AU - Per Sjölin
AU - Fernando Soria
TI - Remarks on a theorem by N. Yu. Antonov
JO - Studia Mathematica
PY - 2003
VL - 158
IS - 1
SP - 79
EP - 97
AB - 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.
LA - eng
UR - http://eudml.org/doc/284431
ER -