# Absolutely continuous dynamics and real coboundary cocycles in ${L}^{p}$-spaces, 0 < p < ∞

Ana Alonso; Jialin Hong; Rafael Obaya

Studia Mathematica (2000)

- Volume: 138, Issue: 2, page 121-134
- ISSN: 0039-3223

## Access Full Article

top## Abstract

top## How to cite

topAlonso, Ana, Hong, Jialin, and Obaya, Rafael. "Absolutely continuous dynamics and real coboundary cocycles in $L^p$-spaces, 0 < p < ∞." Studia Mathematica 138.2 (2000): 121-134. <http://eudml.org/doc/216694>.

@article{Alonso2000,

abstract = {Conditions for the existence of measurable and integrable solutions of the cohomology equation on a measure space are deduced. They follow from the study of the ergodic structure corresponding to some families of bidimensional linear difference equations. Results valid for the non-measure-preserving case are also obtained},

author = {Alonso, Ana, Hong, Jialin, Obaya, Rafael},

journal = {Studia Mathematica},

keywords = {integrable cocycles},

language = {eng},

number = {2},

pages = {121-134},

title = {Absolutely continuous dynamics and real coboundary cocycles in $L^p$-spaces, 0 < p < ∞},

url = {http://eudml.org/doc/216694},

volume = {138},

year = {2000},

}

TY - JOUR

AU - Alonso, Ana

AU - Hong, Jialin

AU - Obaya, Rafael

TI - Absolutely continuous dynamics and real coboundary cocycles in $L^p$-spaces, 0 < p < ∞

JO - Studia Mathematica

PY - 2000

VL - 138

IS - 2

SP - 121

EP - 134

AB - Conditions for the existence of measurable and integrable solutions of the cohomology equation on a measure space are deduced. They follow from the study of the ergodic structure corresponding to some families of bidimensional linear difference equations. Results valid for the non-measure-preserving case are also obtained

LA - eng

KW - integrable cocycles

UR - http://eudml.org/doc/216694

ER -

## References

top- [1] A. I. Alonso and R. Obaya, Dynamical description of bidimensional linear systems with a measurable 2-sheet, J. Math. Anal. Appl.212, 154-175 (1997). Zbl0886.58053
- [2] I. Assani, Note on the equation y = (I-T)x, preprint, 1997.
- [3] I. Assani and J. Woś, An equivalent measure for some nonsingular transformations and application, Studia Math. 97, 1-12 (1990). Zbl0718.28006
- [4] R. C. Bradley, On a theorem of K. Schmidt, Statist. Probab. Lett. 24, 9-12 (1995).
- [5] F. E. Browder, On the iteration of transformations in non-compact minimal dynamical systems, Proc. Amer. Math. Soc. 9, 773-780 (1958). Zbl0092.12602
- [6] H. Furstenberg, Strict ergodicity and transformation of the torus, Amer. J. Math. 83, 573-601 (1961). Zbl0178.38404
- [7] W. Gottschalk and G. Hedlund, Topological Dynamics, Amer. Math. Soc. Colloq. Publ. 36, Providence, RI, 1955. Zbl0067.15204
- [8] U. Krengel and M. Lin, On the range of the generator of a markovian semigroup, Math. Z. 185, 553-565 (1984). Zbl0525.60080
- [9] V. P. Leonov, On the dispersion of the time averages of a stationary stochastic process, Teor. Veroyatnost. i Primenen. 6 (1961), 93-101 (in Russian); English transl. in Theory Probab. Appl. 6 (1961).
- [10] M. Lin and R. Sine, Ergodic theory and the functional equation (I-T)x= y , J. Operator Theory 10, 153-166 (1983). Zbl0553.47006
- [11] F. J. Martín-Reyes and A. de la Torre, On the pointwise ergodic theorem, Studia Math. 108, 1-4 (1994). Zbl0861.28011
- [12] S. Novo and R. Obaya, An ergodic classification of bidimensional linear systems, J. Dynam. Differential Equations 8, 373-406 (1996). Zbl0869.28009
- [13] S. Novo and R. Obaya, An ergodic and topological approach to almost periodic bidimensional linear systems, in: Contemp. Math. 215, Amer. Math. Soc., 1998, 299-323. Zbl0896.58041
- [14] R. Sato, Pointwise ergodic theorems in Lorentz spaces L(p,q) for null preserving transformations, Studia Math. 114, 227-236 (1995). Zbl0835.47006