Geodesic
On absolute convergence of multiple Fourier series
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2015), pp. 12-21 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider absolute convergence of multiple series of Fourier–Haar coefficients for functions of many variables with partial derivatives of higher order. It is shown that the obtained results are best possible for general orthonormal systems.
Mots-clés : Fourier coefficients
Keywords: Haar system, partial derivatives, general orthonormal systems. 
@article{IVM_2015_9_a1,
     author = {L. D. Gogoladze and V. Sh. Tsagareishvili},
     title = {On absolute convergence of multiple {Fourier} series},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {12--21},
     year = {2015},
     number = {9},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2015_9_a1/}
}
TY  - JOUR
AU  - L. D. Gogoladze
AU  - V. Sh. Tsagareishvili
TI  - On absolute convergence of multiple Fourier series
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2015
SP  - 12
EP  - 21
IS  - 9
UR  - http://geodesic.mathdoc.fr/item/IVM_2015_9_a1/
LA  - ru
ID  - IVM_2015_9_a1
ER  - 
%0 Journal Article
%A L. D. Gogoladze
%A V. Sh. Tsagareishvili
%T On absolute convergence of multiple Fourier series
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2015
%P 12-21
%N 9
%U http://geodesic.mathdoc.fr/item/IVM_2015_9_a1/
%G ru
%F IVM_2015_9_a1
L. D. Gogoladze; V. Sh. Tsagareishvili. On absolute convergence of multiple Fourier series. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2015), pp. 12-21. http://geodesic.mathdoc.fr/item/IVM_2015_9_a1/

[1] Kashin B. S., Saakyan A. A., Ortogonalnye ryady, AFS, M., 1999

[2] Gogoladze L., Tsagareishvili V., “Absolute convergence of multiple Fourier–Haar series”, Georgian Math. J., 21:1 (2014), 69–74 | DOI | MR | Zbl

[3] Kachmazh S., Shteingauz G., Teoriya ortogonalnykh ryadov, GIFML, M., 1958

[4] Gogoladze L., Tsagareishvili V., “Absolyutnaya skhodimost ryadov Fure–Khaara funktsii dvukh peremennykh”, Izv. vuzov. Matem., 2008, no. 5, 14–25 | MR | Zbl

[5] Ulyanov P. L., “O ryadakh po sisteme Khaara”, Matem. sb., 63(105):3 (1964), 356–391 | MR | Zbl