On multiparameter Chacon's type ergodic theorems

The purpose of this paper is to deal with generalizations of ratio ergodic theorems due to R.V. Chacon, G. Baxter, and K. Jacobs. We prove two weighted generalizations of the Chacon ergodic theorem and the Jacobs random ergodic theorem. L. Sucheston has formulated a general principle yielding simultaneous proofs of many almost everywhere multiparameter convergence theorems. This principle will allow us to derive multiparameter Chacon's type ergodic theorems for positive linear contractions on L-1. The advantage is that we can inquire further into the problem of improving the multiparameter Chacon-Ornstein ergodic theorem due to Frangos and Sucheston. A multiparameter generalization of the Dunford Schwartz ergodic theorem is also obtained. In addition, our consideration comes to the a.e. convergence for sectorially restricted averages in the commutative case, as in the Brunel Dunford Schwartz theorem. Moreover, we establish two Chacon's type nonlinear ergodic theorems for the nonlinear sums of affine operators on L-1.