Geodesic
An~example of an orthonormal system of convergence in~$C$ but not in~$L^2$
Sbornik. Mathematics, Tome 20 (1973) no. 1, pp. 145-153

Voir la notice de l'article provenant de la source Math-Net.Ru

We prove the following theorem. Theorem. {\it For any $p_0\in[1,\infty)$ there exists a complete uniformly bounded orthonormal system $\{\varphi_n\}$ having the following properties}: 1) For all $f\in L^p, p>p_0,$ the Fouries series $\sum c_n\varphi_n$ converges to $f$ almost everywhere. 2) {\it There exists an $F\in L^{p_0}$ whose Fourier series diverges almost everywhere.} Bibliography: 8 titles. 
@article{SM_1973_20_1_a7,
     author = {A. M. Olevskii},
     title = {An~example of an orthonormal system of convergence in~$C$ but not in~$L^2$},
     journal = {Sbornik. Mathematics},
     pages = {145--153},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {1973},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1973_20_1_a7/}
}
TY  - JOUR
AU  - A. M. Olevskii
TI  - An~example of an orthonormal system of convergence in~$C$ but not in~$L^2$
JO  - Sbornik. Mathematics
PY  - 1973
SP  - 145
EP  - 153
VL  - 20
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1973_20_1_a7/
LA  - en
ID  - SM_1973_20_1_a7
ER  - 
%0 Journal Article
%A A. M. Olevskii
%T An~example of an orthonormal system of convergence in~$C$ but not in~$L^2$
%J Sbornik. Mathematics
%D 1973
%P 145-153
%V 20
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1973_20_1_a7/
%G en
%F SM_1973_20_1_a7
A. M. Olevskii. An~example of an orthonormal system of convergence in~$C$ but not in~$L^2$. Sbornik. Mathematics, Tome 20 (1973) no. 1, pp. 145-153. http://geodesic.mathdoc.fr/item/SM_1973_20_1_a7/