论文标题
平均发散的网格方法
Grid method for divergence of averages
论文作者
论文摘要
In this paper, we will introduce the `grid method' to prove that the extreme case of oscillation occurs for the averages obtained by sampling a flow along the sequence of times of the form $\{n^α: n\in \mathbb{N}\}$, where $α$ is a positive non-integer rational number.序列的这种行为称为“强大的属性”。通过使用相同的方法，我们将举一个一般类序列的示例，该序列满足“强扫除”属性。这类序列对于解决长期存在的开放问题可能很有用：对于给定的非理性$α$，无论序列$ $（n^α）$是否对$ l^p $``尖端''不好。在证明这些结果的过程中，我们将证明该原理的连续版本。
In this paper, we will introduce the `grid method' to prove that the extreme case of oscillation occurs for the averages obtained by sampling a flow along the sequence of times of the form $\{n^α: n\in \mathbb{N}\}$, where $α$ is a positive non-integer rational number. Such behavior of a sequence is known as the `strong sweeping out property'. By using the same method, we will give an example of a general class of sequences which satisfy the `strong sweeping out' property. This class of sequences may be useful to solve the longstanding open problem: for a given irrational $α$, whether the sequence $(n^α)$ is `pointwise bad' for $L^p$ or not. In the process of proving these results, we will prove a continuous version of the Conze principle.
