Geodesic
Fundamental function of Rademacher spaces
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2014), pp. 38-46.

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

In this paper we study the norm of Rademacher sums for some class of rearrangement invariant spaces and find its asymptotic behavior with the growth of the number of summands.
Keywords: Rademacher space, rearrangement invariant space, Lorentz space
Mots-clés : Marcinkiewicz space. 
@article{IVM_2014_2_a4,
     author = {A. I. Novikova},
     title = {Fundamental function of {Rademacher} spaces},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {38--46},
     publisher = {mathdoc},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2014_2_a4/}
}
TY  - JOUR
AU  - A. I. Novikova
TI  - Fundamental function of Rademacher spaces
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2014
SP  - 38
EP  - 46
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2014_2_a4/
LA  - ru
ID  - IVM_2014_2_a4
ER  - 
%0 Journal Article
%A A. I. Novikova
%T Fundamental function of Rademacher spaces
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2014
%P 38-46
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2014_2_a4/
%G ru
%F IVM_2014_2_a4
A. I. Novikova. Fundamental function of Rademacher spaces. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2014), pp. 38-46. http://geodesic.mathdoc.fr/item/IVM_2014_2_a4/

[1] Rademacher H., “Einige Sätze über Reihen von allgemeinen Orthogonalfunktionen”, Math. Ann., 87 (1922), 111–138 | DOI | MR

[2] Rodin V. A., Semenov E. M., “Rademacher series in symmetric spaces”, Anal. Math., 1 (1975), 207–222 | DOI | MR | Zbl

[3] Braverman M. Sh., “Dopolnyaemost podprostranstv, porozhdennykh nezavisimymi funktsiyami v simmetrichnykh prostranstvakh”, Funkts. analiz i ego prilozh., 16:2 (1982), 66–67 | MR | Zbl

[4] Raynaud Y., “Complemented hilbertian subspaces in rearrangement invariant function spaces”, Illinois J. of Math., 39:2 (1995), 212–250 | MR | Zbl

[5] Astashkin S. V., Hernandez F. L., Semenov E. M., “Stricktly singular inclusions of rearrangement invariant spaces and Rademacher spaces”, Studia Math., 193:3 (2009), 269–283 | MR | Zbl

[6] Krein S. G., Petunin Yu. I., Semenov E. M., Interpolyatsiya lineinykh operatorov, Nauka, M., 1978 | MR

[7] Lindenstrauss J., Tzafriri L., Classical Banach spaces, v. II, Function spaces, Springer-Verlag, 1979 | MR | Zbl

[8] Lorentz G. G., “Some new functional spaces”, Ann. Math., 51 (1950), 37–55 | DOI | MR | Zbl

[9] Semenov E. M., “Teoremy vlozheniya dlya banakhovykh prostranstv izmerimykh funktsii”, DAN SSSR, 156:6 (1964), 1292–1295 | Zbl

[10] Montgomery-Smith S. J., “The distribution of Rademacher sums”, Proc. Amer. Math. Soc., 109:2 (1990), 517–522 | DOI | MR | Zbl

[11] Astashkin S. V., “Funktsii Rademakhera v simmetrichnykh prostranstvakh”, Funkts. analiz, Sovremennaya matem. Fundament. napr., 32, 2009, 3–161 | MR | Zbl