论文标题
在同质的千古双线性上，$ 1 $结合的乘量重量
On the homogeneous ergodic bilinear averages with $1$-bounded multiplicative weights
论文作者
论文摘要
我们通过证明，对于任何概率空间$（x，y Mathcal bb b b b的$ nyth $ b，b b b b b b b b b，b b b b b b b b b b b b b b b b $ b b b b b b b b b b b b $boldsymbolν$），我们建立了波尔加因双重复发定理和厄格贡式波尔加因 - 萨纳克的定理的概括。 \在l^2（x）$中，几乎所有$ x \ in x $中，我们都有\ [\ frac {1} {n} {n} \ sum_ {n = 1}^{n} \boldsymbolν（n） 0. \]我们进一步证明了他的双重复发定理证明他的关键要素。
We establish a generalization of Bourgain double recurrence theorem and ergodic Bourgain-Sarnak's theorem by proving that for any aperiodic $1$-bounded multiplicative function $\boldsymbolν$, for any map $T$ acting on a probability space $(X,\mathcal{A},μ)$, for any integers $a,b$, for any $f,g \in L^2(X)$, and for almost all $x \in X$, we have \[\frac{1}{N} \sum_{n=1}^{N} \boldsymbolν(n) f(T^{a n}x)g(T^{bn}x) \xrightarrow[N\rightarrow +\infty]{} 0.\] We further present with proof the key ingredients of Bourgain's proof of his double recurrence theorem.
