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@article{MZM_2008_83_5_a9, author = {G. E. Tkebuchava and K. Finet}, title = {Unconditional {Convergence} of {Fourier} {Expansions} in {Systems} of {Product} {Bases} in {Orlicz} {Spaces}}, journal = {Matemati\v{c}eskie zametki}, pages = {741--751}, publisher = {mathdoc}, volume = {83}, number = {5}, year = {2008}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/MZM_2008_83_5_a9/} }
TY - JOUR AU - G. E. Tkebuchava AU - K. Finet TI - Unconditional Convergence of Fourier Expansions in Systems of Product Bases in Orlicz Spaces JO - Matematičeskie zametki PY - 2008 SP - 741 EP - 751 VL - 83 IS - 5 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/MZM_2008_83_5_a9/ LA - ru ID - MZM_2008_83_5_a9 ER -
G. E. Tkebuchava; K. Finet. Unconditional Convergence of Fourier Expansions in Systems of Product Bases in Orlicz Spaces. Matematičeskie zametki, Tome 83 (2008) no. 5, pp. 741-751. http://geodesic.mathdoc.fr/item/MZM_2008_83_5_a9/
[1] B. S. Kashin, A. A. Saakyan, Ortogonalnye ryady, AFTs, M., 1999 | MR | Zbl
[2] Y. Meyer, Wavelets and Operators, Cambridge Stud. Adv. Math., 37, Cambridge Univ. Press, Cambridge, 1992 | MR | Zbl
[3] P. Wojtaszczyk, A Mathematical Introduction to Wavelets, London Math. Soc. Stud. Texts, 37, Cambridge Univ. Press, Cambridge, 1997 | MR | Zbl
[4] M. Dei, Normirovannye lineinye prostranstva, IL, M., 1961 | MR | Zbl
[5] S. V. Bochkarev, “Suschestvovanie bazisa v prostranstve funktsii, analiticheskikh v kruge, i nekotorye svoistva sistemy Franklina”, Matem. sb., 95:1 (1974), 3–18 | MR | Zbl
[6] S. V. Bochkarev, “Bazisy funktsionalnykh prostranstv i sistema Franklina”, Teoriya funktsii. Materialy vsesoyuznoi shkoly po teorii funktsii, Tr. MIAN, 190, Nauka, M., 1989, 22–39 | MR | Zbl
[7] G. G. Gevorkyan, “Nekotorye teoremy o bezuslovnoi skhodimosti, mazhorante ryadov Franklina i ikh prilozheniyakh k prostranstvam $\operatorname{Re}H_p$”, Teoriya funktsii. Materialy vsesoyuznoi shkoly po teorii funktsii, Tr. MIAN, 190, Nauka, M., 1989, 49–74 | MR | Zbl
[8] D. L. Donoho, “Unconditional bases and bit-level compression”, Appl. Comput. Harmon. Anal., 3:4 (1996), 388–392 | DOI | MR | Zbl
[9] D. L. Donoho, “Unconditional bases are optimal bases for data compression and for statistical estimation”, Appl. Comput. Harmon. Anal., 1:1 (1993), 100–115 | DOI | MR | Zbl
[10] D. L. Donoho, I. M. Johnstone, G. Kerkyacharian, D. Picard, “Wavelet shrinkage: asymptopia?”, J. Roy. Statist. Soc. Ser. B, 57:2 (1995), 301–369 | MR | Zbl
[11] S. Karlin, “Bases in Banach spaces”, Duke Math. J., 15:4 (1948), 971–985 | DOI | MR | Zbl
[12] A. Pelczynski, “Projections in certain Banach spaces”, Studia Math., 19 (1960), 209–228 | MR | Zbl
[13] P. L. Uljanov, “Haar series and related questions”, Alfred Haar memorial conference, vol. I, II (Budapest, 1985), Colloq. Math. Soc. János Bolyai, 49, North-Holland, Amsterdam, 1987, 57–96 | MR | Zbl
[14] B. I. Golubov, “Ryady po sisteme Khaara”, Itogi nauki i tekhniki. Matem. analiz, VINITI, M., 1971, 109–146 | MR | Zbl
[15] W. R. Wade, “Recent developments in the theory of Haar series”, Colloq. Math., 52:2 (1987), 213–238 | MR | Zbl
[16] A. M. Olevskii, “Ryady Fure i funktsii Lebega”, UMN, 22:3 (1967), 237–239 | MR
[17] A. M. Olevskii, Fourier Series With Respect to General Orthogonal Systems, Ergeb. Math. Grenzgeb., 86, Springer-Verlag, Berlin, 1975 | MR | Zbl
[18] D. L. Burkholder, “A proof of Pelczynski's conjecture for the Haar system”, Studia Math., 91:1 (1988), 79–83 | MR | Zbl
[19] V. F. Gaposhkin, “O suschestvovanii bezuslovnykh bazisov v prostranstvakh Orlicha”, Funkts. analiz i prilozh., 1:4 (1967), 26–32 | MR | Zbl
[20] V. F. Gaposhkin, “O bezuslovnykh bazisakh v prostranstvakh Orlicha”, Sib. matem. zhurn., 9:2 (1968), 280–287 | Zbl
[21] S. V. Bochkarev, “O bezuslovnykh bazisakh”, Matem. zametki., 1 (1967), 391–398 | MR | Zbl
[22] M. A. Krasnoselskii, Ya. B. Rutitskii, Vypuklye funktsii i prostranstva Orlicha, Sovrem. problemy matem., Fizmatgiz, M., 1958 | MR | Zbl
[23] O. D. Tsereteli, “Ob integriruemosti sopryazhennoi funktsii”, Tr. Tbilisskogo matem. in-ta im. A. M. Razmadze AN GrSSR, 43 (1973), 149–168 | MR | Zbl
[24] A. Zigmund, Trigonometricheskie ryady, t. 1, 2, Mir, M., 1965 | MR | Zbl
[25] Z. Ciesielski, “Constructive function theory and spline system”, Studia Math., 53:3 (1975), 277–302 | MR | Zbl
[26] C. Finet, G. Tkebuchava, “Some classical function systems in separable Orlicz spaces”, Studia Math., 121:2 (1996), 193–205 | MR | Zbl
[27] D. L. Burkholder, R. F. Gundy, “Extrapolation and interpolation of quasi-linear operators on martingales”, Acta Math., 124:1 (1970), 249–304 | DOI | MR | Zbl
[28] D. L. Burkholder, “Distribution function inequalities for martingales”, Ann. Probab., 1:1 (1973), 19–42 | DOI | MR | Zbl
[29] G. E. Tkebuchava, “O bezuslovnoi skhodimosti po sistemam proizvedenii bazisov”, Matem. sb., 183:10 (1992), 109–122 | MR | Zbl
[30] J. Marcinkiewicz, “Quelques théorèms sur les séries orthogonales”, Ann. Soc. Polon. Math., 16 (1938), 84–96 | Zbl
[31] S. Yano, “On a lemma of Marcinkiewicz and its applications to Fourier series”, Tohoku Math. J. (2), 11:2 (1959), 191–215 | DOI | MR | Zbl
[32] Z. Ciesielski, P. Simon, P. Sjölin, “Equivalence of Haar and Franklin systems in $L^p$ spaces”, Studia Math., 60:2 (1977), 195–210 | MR | Zbl
[33] G. E. Tkebuchava, “O bazisakh v prostranstvakh Orlicha”, Anal. Math., 7:1 (1981), 69–80 | DOI | MR | Zbl