Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
Let τ be a null preserving point transformation on a finite measure space. Assuming τ is invertible, P. Ortega Salvador has recently obtained sufficient conditions for the almost everywhere convergence of the ergodic averages in $L_{pq}$ with 1 < p < ∞, 1 < q < ∞. In this paper we obtain necessary and sufficient conditions for the almost everywhere convergence, without assuming that τ is invertible and only assuming that p ≠ ∞.
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
209-216
Opis fizyczny
Daty
wydano
1994
otrzymano
1993-09-09
poprawiono
1993-11-09
Twórcy
autor
- Department of Mathematics, School of Science, Okayama University, Okayama 700, Japan
Bibliografia
- [1] R. V. Chacon, A class of linear transformations, Proc. Amer. Math. Soc. 15 (1964), 560-564.
- [2] N. Dunford and J. T. Schwartz, Linear Operators. Part I: General Theory, Interscience, New York, 1958.
- [3] A. M. Garsia, Topics in Almost Everywhere Convergence, Markham, Chicago, 1970.
- [4] R. A. Hunt, On L(p,q) spaces, Enseign. Math. 12 (1966), 249-276.
- [5] U. Krengel, Ergodic Theorems, Walter de Gruyter, Berlin, 1985.
- [6] P. Ortega Salvador, Weights for the ergodic maximal operator and a.e. convergence of the ergodic averages for functions in Lorentz spaces, Tôhoku Math. J. 45 (1993), 437-446.
- [7] C. Ryll-Nardzewski, On the ergodic theorems. I. (Generalized ergodic theorems), Studia Math. 12 (1951), 65-73.
- [8] R. Sato, On pointwise ergodic theorems for positive operators, ibid. 97 (1990), 71-84.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv109i2p209bwm