Sparse Rademacher chaos in symmetric spaces

S. V. Astashkin ; K. V. Lykov

Algebra i analiz, Tome 28 (2016) no. 1, pp. 3-31.

Bibliographie

[1] Khintchine A., “Über dyadische Bruche”, Math. Z., 18:1 (1923), 109–116 | DOI | MR | Zbl

[2] Rodin V. A., Semyonov E. M., “Rademacher series in symmetric spaces”, Anal. Math., 1:3 (1975), 207–222 | DOI | MR | Zbl

[3] Kwapien S., Woyczijnski W. A., Random series and stochastic integrals: single and multiple, Birkhauser, Boston, MA, 1992 | MR | Zbl

[4] Golubov B. I., Efimov A. V., Skvortsov V. A., Ryady i preobrazovaniya Uolsha: teoriya i primeneniya, Izd-vo LKI, M., 2008

[5] Astashkin S. V., Sukhanov R. C., “O nekotorykh svoistvakh khaosa Rademakhera”, Mat. zametki, 91:5 (2012), 654–666 | DOI | MR | Zbl

[6] Astashkin S. V., “Rademacher chaos in symmetric spaces”, East J. Approx., 4:3 (1998), 311–336 | MR | Zbl

[7] Astashkin S. V., “Rademacher chaos in symmetric spaces. II”, East J. Approx., 6:1 (2000), 71–86 | MR | Zbl

[8] Astashkin S. V., “Funktsii Rademakhera v simmetrichnykh prostranstvakh”, Sovrem. mat. Fundam. napravleniya, 32, 2009, 3–161 | MR | Zbl

[9] Blei R., “Fractional Cartesian products of sets”, Ann. Inst. Fourier (Grenoble), 29:2 (1979), 79–105 | DOI | MR | Zbl

[10] Blei R., “Combinatorial dimension and certain norms in harmonic analysis”, Amer. J. Math., 106:4 (1984), 847–887 | DOI | MR | Zbl

[11] Blei R., Analysis in integer and fractional dimensions, Cambridge Stud. Adv. Math., 71, Cambridge Univ. Press, Cambridge, 2001 | MR | Zbl

[12] Erdos P., “On extremal problem of graphs and generalized graphs”, Israel J. Math., 2:3 (1964), 183–190 | DOI | MR | Zbl

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

[14] Lindenstrauss J., Tzafriri L., Classical Banach spaces, v. II, Ergeb. (3), Math. Grenzgeb., 97, Function spaces, Springer-Verlag, Berlin, 1979 | MR | Zbl

[15] Bennett C., Sharpley R., Interpolation of operators, Pure Appl. Math., 129, Acad. Press, Boston, 1988 | MR | Zbl

[16] Kashin B. S., Saakyan A. A., Ortogonalnye ryady, Izd-vo AFTs, M., 1999 | MR

[17] Braverman M. Sh., Independent random variables and rearrangement invariant spaces, London Math. Soc. Lecture Note Ser., 194, Cambridge Univ. Press, Cambridge, 1994 | MR | Zbl

[18] Kovari T., Sos V. T., Turan P., “On a problem of K. Zarankiewicz”, Colloq. Math., 3:1 (1954), 50–57 | MR | Zbl

[19] Blei R., Janson S., “Rademacher chaos: tail estimates versus limit theorem”, Ark. Mat., 42:1 (2004), 13–29 | DOI | MR | Zbl

[20] Blei R., Ge L., “Relationships between combinatorial measurements and Orlicz norms”, J. Funct. Anal., 257:3 (2009), 683–720 | DOI | MR | Zbl

[21] Blei R., Ge L., “Relationships between combinatorial measurements and Orlicz norms. II”, J. Funct. Anal., 257:12 (2009), 3949–3967 | DOI | MR | Zbl

[22] Blei R., “Measurements of interdependence”, Lith. Math. J., 51:2 (2011), 141–154 | DOI | MR | Zbl

[23] Bonami A., “Ensembles $\Lambda(p)$ dans de dual de $D^\infty$”, Ann. Inst. Fourier (Grenoble), 18:2 (1968), 193–204 | DOI | MR | Zbl

[24] Bonami A., “Étude des coefficients de Fourier des fonctions de $L^p(G)$”, Ann. Inst. Fourier (Grenoble), 20:2 (1970), 335–402 | DOI | MR | Zbl

[25] Shiryaev A. N., Veroyatnost-$1$, MTsNMO, M., 2004

[26] Milman M., Extrapolation and optimal decompositions with applications to analysis, Lecture Notes Math., 1580, Springer-Verlag, Berlin, 1994 | MR | Zbl

[27] Astashkin S. V., “Ekstrapolyatsionnye funktory na semeistve shkal, porozhdennykh veschestvennym metodom interpolyatsii”, Sib. mat. zh., 46:2 (2005), 264–289 | MR | Zbl

[28] Astashkin S. V., Lykov K. V., “Extrapolation description of rearrangement invariant spaces and related problems”, Banach and function spaces III (ISBFS, 2009), Yokohama Publ., Yokohama, 2011, 1–52 | MR | Zbl

[29] Zigmund A., Trigonometricheskie ryady, v. 1, Mir, M., 1965 | MR