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1998 | 128 | 2 | 145-157
Tytuł artykułu

Dominated ergodic theorems in rearrangement invariant spaces

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study conditions under which Dominated Ergodic Theorems hold in rearrangement invariant spaces. Consequences for Orlicz and Lorentz spaces are given. In particular, our results generalize the classical theorems for the spaces $L_p$ and the classes $L log^nL$.
Czasopismo
Rocznik
Tom
128
Numer
2
Strony
145-157
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-01-30
poprawiono
1997-08-28
Twórcy
  • Department of Mathematics & Computer Sciences, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel, braver@indigo.cs.bgu.ac.il
  • Department of Mathematics & Computer Sciences, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel, benzion@indigo.cs.bgu.ac.il
  • Department of Mathematics, Tashkent State University, Tashkent, Uzbekistan
Bibliografia
  • [AM90] M. Ariño and B. Muckenhoupt, Maximal functions on classical Lorentz spaces and Hardy's inequality with weights for nonincreasing functions, Trans. Amer. Math. Soc. 320 (1990), 727-735.
  • [B93] M. Braverman, On a class of operators, J. London Math. Soc. 47 (1993), 119-128.
  • [BM77] M. Braverman and A. Mekler, On the Hardy-Littlewood property of symmetric spaces, Siberian Math. J. 18 (1977), 371-385.
  • [C66] A. P. Calderón, Spaces between $L^1$ and $L^∞$ and the theorem of Marcinkiewicz, Studia Math. 26 (1966), 273-299.
  • [Do53] J. L. Doob, Stochastic Processes, Wiley, New York, 1953.
  • [De73] Y. Derriennic, On integrability of the supremum of ergodic ratios, Ann. Probab. 1 (1973), 338-340.
  • [DS58] N. Dunford and J. Schwartz, Linear Operators, part I, Interscience, New York, 1958.
  • [ES92] G. A. Edgar and L. Sucheston, Stopping Times and Directed Processes, Encyclopedia Math. Appl., Cambridge Univ. Press, 1992.
  • [G86] D. Gilat, The best bound in the L logL inequality of Hardy and Littlewood and its martingale counterpart, Proc. Amer. Math. Soc. 97 (1986), 429-436.
  • [KR61] M. A. Krasnosel'skiĭ and Ya. B. Rutitskiĭ, Convex Functions and Orlicz Spaces, Noordhoff, 1961.
  • [KPS82] S. G. Krein, Yu. Petunin and E. Semenov, Interpolation of Linear Operators, Transl. Math. Monographs 54, Amer. Math. Soc., Providence, 1982.
  • [K85] U. Krengel, Ergodic Theorems, de Gruyter Stud. Math., de Gruyter, Berlin, 1985.
  • [LT79] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces. Function Spaces, Springer, 1979.
  • [M65] B. S. Mityagin, An interpolation theorem for modular spaces, Mat. Sb. 66 (1965), 473-482 (in Russian).
  • [O71] D. S. Ornstein, A remark on the Birkhoff ergodic theorem, Illinois J. Math. 15 (1971), 77-79.
  • [Sa90] E. T. Sawyer, Boundedness of classical operators in classical Lorentz spaces, Studia Math. 96 (1990), 145-158.
  • [SW71] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton, N.J., 1971.
  • [St93] V. D. Stepanov, The weighted Hardy's inequality for nonincreasing functions, Trans. Amer. Math. Soc. 338 (1993), 173-186.
  • [V85] A. Veksler, An ergodic theorem in symmetric spaces, Sibirsk. Mat. Zh. 24 (1985), 189-191 (in Russian).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv128i2p145bwm
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