Geodesic
On unconditional convergence with respect to systems of products of bases
Sbornik. Mathematics, Tome 77 (1994) no. 1, pp. 231-244 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Decisive conditions are established for unconditionality of expansions with respect to bases in spaces of functions of several variables. The properties of the multiple Haar and Franklin systems are studied. 
@article{SM_1994_77_1_a13,
     author = {G. E. Tkebuchava},
     title = {On unconditional convergence with respect to systems of products of bases},
     journal = {Sbornik. Mathematics},
     pages = {231--244},
     year = {1994},
     volume = {77},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1994_77_1_a13/}
}
TY  - JOUR
AU  - G. E. Tkebuchava
TI  - On unconditional convergence with respect to systems of products of bases
JO  - Sbornik. Mathematics
PY  - 1994
SP  - 231
EP  - 244
VL  - 77
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1994_77_1_a13/
LA  - en
ID  - SM_1994_77_1_a13
ER  - 
%0 Journal Article
%A G. E. Tkebuchava
%T On unconditional convergence with respect to systems of products of bases
%J Sbornik. Mathematics
%D 1994
%P 231-244
%V 77
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1994_77_1_a13/
%G en
%F SM_1994_77_1_a13
G. E. Tkebuchava. On unconditional convergence with respect to systems of products of bases. Sbornik. Mathematics, Tome 77 (1994) no. 1, pp. 231-244. http://geodesic.mathdoc.fr/item/SM_1994_77_1_a13/

[1] Kashin B. S., Saakyan A. A., Ortogonalnye ryady, Nauka, M., 1984 | MR | Zbl

[2] Marcinkiewicz J., “Quelques theorems sur les series orthogonales”, Ann. Soc. Polon. Math., 16 (1937), 85–96

[3] Gaposhkin V. F., “O sisteme Khaara, kak bezuslovnom bazise v $L^p $”, Matem. zametki, 15:2 (1974), 191– 196 | MR | Zbl

[4] Bochkarev S. V., “O bezuslovnykh bazisakh”, Matem. zametki, 1:4 (1967), 391–398 | MR | Zbl

[5] Gaposhkin V. F., “Bezuslovnye bazisy v prostranstvakh Orlicha”, UMN, 22 (1967), 113–114 | MR

[6] Bochkarev S. V., “Suschestvovanie bazisa v prostranstve funktsii, analiticheskikh v kruge, i nekotorye svoistva sistemy Franklina”, Matem. sb., 95(137) (1974), 3–18 | MR | Zbl

[7] Gaposhkin V. F., “O suschestvovanii bezuslovnykh bazisov v prostranstvakh Orlicha”, Funktsion. analiz i ego pril., 1:4 (1967), 26–32 | MR | Zbl

[8] Olevskii A. M., Fourier series with respect to general orthogonal systems, Springer, Berlin–Heidelberg–New-York, 1975 | MR | Zbl

[9] Karlin S., “Bases in Banach spaces”, Duke Math. J., 15 (1948), 971–985 | DOI | MR | Zbl

[10] Pelchynski A., “Projection in certain Banach spaces”, Studia Math., 19 (1960), 209–228 | MR

[11] Gevorkyan G. G., “Nekotorye teoremy o bezuslovnoi skhodimosti i mazhorante ryadov Franklina i ikh primeneniya k prostranstvam $\operatorname{Re}H_p$”, Tr. MIAN, 190, Nauka, M., 1989, 49–74 | MR | Zbl

[12] Burkcholder D., Gundy R., “Extrapolation and interpolation of quasi linear operators on martingales”, Acta Math., 124 (1970), 249–304 | DOI | MR

[13] Edvars R., Ryady Fure, T. 2, Mir, M, 1985

[14] Krasnoselskii M. A., Rutitskii Ya. B., Vypuklye funktsii i prostranstva Orlicha, Fizmatgiz, M., 1958 | MR

[15] Tkebuchava G. E., “O svoistvakh bazisov v prostranstvakh Orlicha”, Analysis Math., 7:1 (1986), 69–80 | DOI | MR

[16] Getsadze R. D., “O raskhodimosti po mere kratnykh ryadov Fure”, Nekotorye voprosy teorii funktsii i funk. analiza, T. 4, TGU, Tbilisi, 1988, 59–76

[17] Tkebuchava G. E., “O kratnykh sistemakh funktsii v prostranstvakh Orlicha”, Nekotorye voprosy teorii funktsii i funk. analiza, T. 4, TGU, Tbilisi, 1988, 194–206

[18] Tkebuchava G. E., “O bezuslovnykh bazisakh v funktsionalnykh prostranstvakh”, Nekotorye voprosy teorii funktsii i funk. analiza, T. 4, TGU, Tbilisi, 1988, 207–224

[19] Garsia A., Topics in almost everywhere convergence, Makhram Publ. Co., Chicago, 1970 | MR

[20] Karagulyan G. G., “O raskhodimosti dvoinykh ryadov Fure po polnym ortonormirovannym sistemam”, Izv. AN ArmSSR. Matematika, 24:2 (1988), 147–159 | MR

[21] Tkebuchava G., “On unconditional convergence of Haar series”, Approxim. Theory, Banach Center Publ., 4, Warszawa, 1988, 261–272 | MR

[22] Zigmund A., Trigonometricheskie ryady, T. 1, Mir, M., 1965 | MR