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Dominated ergodic theorems in rearrangement invariant spaces

Michael Braverman; Ben-Zion Rubshtein; Alexander Veksler

Studia Mathematica (1998)

  • Volume: 128, Issue: 2, page 145-157
  • ISSN: 0039-3223

Abstract

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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 l o g n L .

How to cite

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Braverman, Michael, Rubshtein, Ben-Zion, and Veksler, Alexander. "Dominated ergodic theorems in rearrangement invariant spaces." Studia Mathematica 128.2 (1998): 145-157. <http://eudml.org/doc/216480>.

@article{Braverman1998,
abstract = {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 $L log^nL$.},
author = {Braverman, Michael, Rubshtein, Ben-Zion, Veksler, Alexander},
journal = {Studia Mathematica},
keywords = {rearrangement invariant space; ergodic theorem; Hardy-Littlewood property; dominated ergodic theorems; rearrangement invariant spaces; Orlicz and Lorentz spaces},
language = {eng},
number = {2},
pages = {145-157},
title = {Dominated ergodic theorems in rearrangement invariant spaces},
url = {http://eudml.org/doc/216480},
volume = {128},
year = {1998},
}

TY - JOUR
AU - Braverman, Michael
AU - Rubshtein, Ben-Zion
AU - Veksler, Alexander
TI - Dominated ergodic theorems in rearrangement invariant spaces
JO - Studia Mathematica
PY - 1998
VL - 128
IS - 2
SP - 145
EP - 157
AB - 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 $L log^nL$.
LA - eng
KW - rearrangement invariant space; ergodic theorem; Hardy-Littlewood property; dominated ergodic theorems; rearrangement invariant spaces; Orlicz and Lorentz spaces
UR - http://eudml.org/doc/216480
ER -

References

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  15. [O71] D. S. Ornstein, A remark on the Birkhoff ergodic theorem, Illinois J. Math. 15 (1971), 77-79. Zbl0212.40102
  16. [Sa90] E. T. Sawyer, Boundedness of classical operators in classical Lorentz spaces, Studia Math. 96 (1990), 145-158. Zbl0705.42014
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  18. [St93] V. D. Stepanov, The weighted Hardy's inequality for nonincreasing functions, Trans. Amer. Math. Soc. 338 (1993), 173-186. Zbl0786.26015
  19. [V85] A. Veksler, An ergodic theorem in symmetric spaces, Sibirsk. Mat. Zh. 24 (1985), 189-191 (in Russian). Zbl0603.28017

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