Pointwise convergence of some multiple ergodic averages
نویسندگان
چکیده
منابع مشابه
Pointwise Convergence of Some Multiple Ergodic Averages
We show that for every ergodic system (X, μ,T1, . . . ,Td) with commuting transformations, the average 1 Nd+1 ∑ 0≤n1,...,nd≤N−1 ∑ 0≤n≤N−1 f1(T n 1 d ∏ j=1 T n j j x) f2(T n 2 d ∏ j=1 T n j j x) · · · fd(T n d d ∏ j=1 T n j j x). converges for μ-a.e. x ∈ X as N → ∞. If X is distal, we prove that the average 1 N N ∑ i=0 f1(T n 1 x) f2(T n 2 x) · · · fd(T n d x) converges for μ-a.e. x ∈ X as N → ∞...
متن کاملConvergence of Multiple Ergodic Averages for Some Commuting Transformations
We prove the L convergence for the linear multiple ergodic averages of commuting transformations T1, . . . , Tl, assuming that each map Ti and each pair TiT −1 j is ergodic for i 6= j. The limiting behavior of such averages is controlled by a particular factor, which is an inverse limit of nilsystems. As a corollary we show that the limiting behavior of linear multiple ergodic averages is the s...
متن کاملPointwise Convergence of Ergodic Averages in Orlicz Spaces
converge a.e. for all f in L log log(L) but fail to have a finite limit for an f ∈ L. In fact, we show that for each Orlicz space properly contained in L, 1 ≤ q < ∞, there is a sequence along which the ergodic averages converge for functions in the Orlicz space, but diverge for all f ∈ L . This extends the work of K. Reinhold, who, building on the work of A. Bellow, constructed a sequence for w...
متن کاملConvergence of weighted polynomial multiple ergodic averages
In this article we study weighted polynomial multiple ergodic averages. A sequence of weights is called universally good if any polynomial multiple ergodic average with this sequence of weights converges in L. We find a necessary condition and show that for any bounded measurable function φ on an ergodic system, the sequence φ(Tnx) is universally good for almost every x. The linear case was cov...
متن کاملMultifractal analysis of some multiple ergodic averages
In this paper we study the multiple ergodic averages 1 n n ∑ k=1 φ(xk, xkq , · · · , xkql−1 ), (xn) ∈ Σm on the symbolic space Σm = {0, 1, · · · ,m− 1}N ∗ where m ≥ 2, l ≥ 2, q ≥ 2 are integers. We give a complete solution to the problem of multifractal analysis of the limit of the above multiple ergodic averages. Actually we develop a non-invariant and non-linear version of thermodynamic forma...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2018
ISSN: 0001-8708
DOI: 10.1016/j.aim.2018.03.022