Pointwise ergodic theorems for functions in Lorentz spaces $L_{pq}$ with p ≠ ∞

• Autorzy: Ryotaro Sato
• Języki publikacji: EN

Abstrakty

EN

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 ≠ ∞.

Słowa kluczowe

EN

pointwise ergodic theorems; $L_{pq}$ spaces; null preserving transformations; measure preserving transformations; positive contractions on $L_1$ spaces

Kategorie tematyczne

• 47A35: Ergodic theory
• 28D05: Measure-preserving transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1994
• Tom: 109
• Numer: 2
• Strony: 209-216

Daty

wydano

1994

otrzymano

1993-09-09

poprawiono

1993-11-09

Twórcy

autor

Ryotaro Sato

• 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.