论文标题
在$ l^p $空间上的解决条件和运营商的力量增长
Resolvent conditions and growth of powers of operators on $L^p$ spaces
论文作者
论文摘要
令$ t $为$ l^p $上的有界线性运算符。我们研究了在解决条件或CESàRO有限假设下$ t $的权力规范的增长率。实际上，在我们的研究中，$ l^p $空间的相关属性是它们的类型和cotype，而$ 1 <p <\ infty $，它们是UMD的事实。一些证据利用Banach空间上的傅立叶乘数，这说明了为什么UMD空间发挥作用。
Let $T$ be a bounded linear operator on $L^p$. We study the rate of growth of the norms of the powers of $T$ under resolvent conditions or Cesàro boundedness assumptions. Actually the relevant properties of $L^p$ spaces in our study are their type and cotype, and for $1<p<\infty$, the fact that they are UMD. Some of the proofs make use of Fourier multipliers on Banach spaces, which explains why UMD spaces come into play.
