@article{TVP_2009_54_3_a6,
author = {R. Jajte},
title = {Operators on $L^p$-spaces determined by filtrations and pointwise ergodic theorems},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {551--566},
year = {2009},
volume = {54},
number = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TVP_2009_54_3_a6/}
}
R. Jajte. Operators on $L^p$-spaces determined by filtrations and pointwise ergodic theorems. Teoriâ veroâtnostej i ee primeneniâ, Tome 54 (2009) no. 3, pp. 551-566. http://geodesic.mathdoc.fr/item/TVP_2009_54_3_a6/
[1] Akcoglu M. A., “A pointwise theorem in $L^p$-spaces”, Canad. J. Math., 27:5 (1975), 1075–1082 | MR | Zbl
[2] Berg I., Lefstrem I., Interpolyatsionnye prostranstva, Mir, M., 1980, 264 pp. | MR
[3] Berkson E., Bourgain J., Gillespie T. A., “On the almost everywhere convergence of ergodic averages for power-bounded operators on $L^p$-subspaces”, Integral Equations Operator Theory, 14:5 (1991), 678–715 | DOI | MR | Zbl
[4] Berkson E., Gillespie T. A., “Stečkin's theorem, transference, and spectral decompositions”, J. Funct. Anal., 70:1 (1987), 140–170 | DOI | MR | Zbl
[5] Burkholder D. L., “Martingale transforms”, Ann. Math. Statist., 37 (1966), 1494–1504 | DOI | MR | Zbl
[6] Burkholder D. L., Chow Y. S., “Iterates of conditional expectation operators”, Proc. Amer. Math. Soc., 12 (1961), 490–495 | DOI | MR | Zbl
[7] Dowson R. H., Spectral Theory of Linear Operators, London Math. Soc. Monogr., 12, Academic Press, New York, 1978, 422 pp. | MR | Zbl
[8] Duncan R., “Some pointwise convergence results in $L^p(\mu)$, $1
\infty$”, Canad. Math. Bull., 20 (1977), 277–284 | MR | Zbl[9] Danford N., Shvarts Dzh., Lineinye operatory. Ch. 1: Obschaya teoriya, IL, M., 1962, 895 pp.
[10] Edwards R. E., Gaudry G. I., Littlewood–Paley and Multiplier Theory, Ergeb. Math. Grenzgeb., 90, Springer-Verlag, Berlin, 1977, 212 pp. | MR | Zbl
[11] Gaposhkin V. F., “Kriterii usilennogo zakona bolshikh chisel dlya klassov statsionarnykh v shirokom smysle protsessov i odnorodnykh sluchainykh polei”, Teoriya veroyatn. i ee primen., 22:2 (1977), 295–319 | MR | Zbl
[12] Gaposhkin V. F., “Ob individualnoi ergodicheskoi teoreme dlya normalnykh operatorov v $L_2$”, Funkts. analiz i ego pril., 15:1 (1981), 18–22 | MR | Zbl
[13] Garsia A. M., Topics in Almost Everywhere Convergence, Markham, Chicago, 1970, 154 pp. | MR | Zbl
[14] Houdré C., “On the spectral SLLN and pointwise ergodic theorem in $L^\alpha$”, Ann. Probab., 20:4 (1992), 1731–1753 | DOI | MR | Zbl
[15] Jajte R., “On the existence of the ergodic Hilbert transform”, Ann. Probab., 15:2 (1987), 831–835. | DOI | MR | Zbl
[16] Katznelson Y., An Introduction to Harmonic Analysis, Dover, New York, 1976, 264 pp. | MR | Zbl
[17] Millar P. W., “Martingale integrals”, Trans. Amer. Math. Soc., 133 (1968), 145–166 | DOI | MR | Zbl
[18] Stein E. M., Topics in Harmonic Analysis Related to the Littlewood–Paley Theory, Ann. of Math. Stud., 63, Princeton Univ. Press, Princeton, 1970, 146 pp. | MR | Zbl
[19] Zigmund A., Trigonometricheskie ryady, v. 1, Mir, M., 1965, 615 pp. | MR