Geodesic
Convergence of multiple Vilenkin–Fourier series in Lorentz spaces
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 7 (2007) no. 1, pp. 15-22 
O. A. Lukyanenko. Convergence of multiple Vilenkin–Fourier series in Lorentz spaces. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 7 (2007) no. 1, pp. 15-22. http://geodesic.mathdoc.fr/item/ISU_2007_7_1_a3/
@article{ISU_2007_7_1_a3,
     author = {O. A. Lukyanenko},
     title = {Convergence of multiple {Vilenkin{\textendash}Fourier} series in {Lorentz} spaces},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {15--22},
     year = {2007},
     volume = {7},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2007_7_1_a3/}
}
TY  - JOUR
AU  - O. A. Lukyanenko
TI  - Convergence of multiple Vilenkin–Fourier series in Lorentz spaces
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2007
SP  - 15
EP  - 22
VL  - 7
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/ISU_2007_7_1_a3/
LA  - ru
ID  - ISU_2007_7_1_a3
ER  - 
%0 Journal Article
%A O. A. Lukyanenko
%T Convergence of multiple Vilenkin–Fourier series in Lorentz spaces
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2007
%P 15-22
%V 7
%N 1
%U http://geodesic.mathdoc.fr/item/ISU_2007_7_1_a3/
%G ru
%F ISU_2007_7_1_a3

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

Let $\Lambda_{\psi,p}[0,1)^d$ be a near to $L^\infty[0,1)^d$ Lorentz space. We find the function $\tilde\psi$ for which the multiple Vilenkin–Fourier of any $f\in\Lambda_{\psi,p}[0,1)^d$ converge to $f$ in the norm of Lorentz space $\Lambda_{\bar\psi,p}[0,1)^d$.

[1] Lukomskii S. F., “Convergence of Fourier series in Lorentz spaces”, East J. on Aproximat., 9:2 (2003), 229–238 | MR | Zbl

[2] Agaev G. N., Vilenkin N. Ya., Dzhavarli G. M., Rubinshtein A. I., Multiplikativnye sistemy funktsii i garmonicheskogo analiza na nul-mernykh gruppakh, Elm, Baku, 1981 | MR

[3] Luk'yanenko O. A., “O konstantakh Lebega dlya sistemy Vilenkina”, Mekhanika. Matematika: Sb. nauch. tr., 7, Izd-vo Sarat. un-ta, Saratov, 2005, 70

[4] Lukomskii S. F., “O skhodimosti ryadov Fure Uolsha v prostranstvakh, blizkikh k $L_\infty$”, Mat. zametki, 70:6 (2001), 882–889 | DOI | MR

[5] Astashkin S. V., “Ob ekstrapolyatsionnykh svoistvakh shkaly $L_p$-prostranstv”, Mat. sbornik, 194:6 (2003), 23–42 | DOI | MR | Zbl

[6] Lukomskii S. F., “O podposledovatelnostyakh chastichnykh summ ryadov Fure–Uolsha v prostranstvakh Lorentsa”, Izvestiya vuzov. Matematika, 2006, no. 6, 48–55 | MR