A good universal weight for nonconventional ergodic averages in norm

作者：Assani Idris^*; Moore Ryo

来源：Ergodic Theory and Dynamical Systems, 2017, 37(4): 1009-1025.

DOI：10.1017/etds.2015.76

We will show that the sequence appearing in the double recurrence theorem is a good universal weight for the Furstenberg averages. That is, given a system. (X, F, mu, T) and bounded functions f1, f2 is an element of L-infinity (mu), there exists a set of full-measure X (f1), (f2) in X that is independent of integers a and b and a positive integer k such that, for all x is an element of X (f1), (f2), for every other measure-preserving system. (Y, G, nu, S) and for each bounded and measurable function g(1) . . . , g(k) is an element of L-infinity (nu), the averages
1/N Sigma(N)(n=1) f1(T-an x) f2(T-bn x)g(1) circle s(n) g(2) circle s(2n) . . . g(k) circle s(kn)
converge in L-2 (nu).

• 出版日期2017-6