Geodesic
Orthogonal bases in $L^p$
Izvestiya. Mathematics , Tome 4 (1970) no. 5, pp. 1169-1181

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

The following theorem is proved: Given any interval $I\subset[1,2)$, there is an orthonormal system $\{\varphi_n\}$ defined on $[0,1]$ which is a basis in $L^p$ for all $p\in I$, but is not a basis in $L^q$ for any $q\in[1,\infty]\setminus I$. Here $L^\infty=C$. 
@article{IM2_1970_4_5_a9,
     author = {B. V. Ryazanov and A. N. Slepchenko},
     title = {Orthogonal bases in $L^p$},
     journal = {Izvestiya. Mathematics },
     pages = {1169--1181},
     publisher = {mathdoc},
     volume = {4},
     number = {5},
     year = {1970},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1970_4_5_a9/}
}
TY  - JOUR
AU  - B. V. Ryazanov
AU  - A. N. Slepchenko
TI  - Orthogonal bases in $L^p$
JO  - Izvestiya. Mathematics 
PY  - 1970
SP  - 1169
EP  - 1181
VL  - 4
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1970_4_5_a9/
LA  - en
ID  - IM2_1970_4_5_a9
ER  - 
%0 Journal Article
%A B. V. Ryazanov
%A A. N. Slepchenko
%T Orthogonal bases in $L^p$
%J Izvestiya. Mathematics 
%D 1970
%P 1169-1181
%V 4
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1970_4_5_a9/
%G en
%F IM2_1970_4_5_a9
B. V. Ryazanov; A. N. Slepchenko. Orthogonal bases in $L^p$. Izvestiya. Mathematics , Tome 4 (1970) no. 5, pp. 1169-1181. http://geodesic.mathdoc.fr/item/IM2_1970_4_5_a9/