Convergence of Walsh Series in Near-$L^\infty$ Spaces
Matematičeskie zametki, Tome 70 (2001) no. 6, pp. 882-889.

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

We consider near-$L^\infty$ spaces that are the union of Orlicz classes and prove the convergence of Walsh series in such spaces.
@article{MZM_2001_70_6_a6,
     author = {S. F. Lukomskii},
     title = {Convergence of {Walsh} {Series} in {Near-}$L^\infty$ {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {882--889},
     publisher = {mathdoc},
     volume = {70},
     number = {6},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_70_6_a6/}
}
TY  - JOUR
AU  - S. F. Lukomskii
TI  - Convergence of Walsh Series in Near-$L^\infty$ Spaces
JO  - Matematičeskie zametki
PY  - 2001
SP  - 882
EP  - 889
VL  - 70
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2001_70_6_a6/
LA  - ru
ID  - MZM_2001_70_6_a6
ER  - 
%0 Journal Article
%A S. F. Lukomskii
%T Convergence of Walsh Series in Near-$L^\infty$ Spaces
%J Matematičeskie zametki
%D 2001
%P 882-889
%V 70
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2001_70_6_a6/
%G ru
%F MZM_2001_70_6_a6
S. F. Lukomskii. Convergence of Walsh Series in Near-$L^\infty$ Spaces. Matematičeskie zametki, Tome 70 (2001) no. 6, pp. 882-889. http://geodesic.mathdoc.fr/item/MZM_2001_70_6_a6/

[1] Golubov B. I., Efimov A. V., Skvortsov V. A., Ryady Uolsha i preobrazovaniya Uolsha. Teoriya i prilozheniya, Nauka, M., 1987 | Zbl

[2] Finet C., Tkebuchava G. E., “Walsh–Fourier series and their generalizations in Orlicz spaces”, J. Math. Anal. Appl., 221 (1998), 405–418 | DOI | MR | Zbl

[3] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz, Nauka, M., 1977 | Zbl