论文标题
$ l^{p} $空间的$α$ -NUMBER表征
An $α$-number characterization of $L^{p}$ spaces on uniformly rectifiable sets
论文作者
论文摘要
我们给出$ l^{p}（σ）$的特征，用于使用Tolsa的$α$ -NUMBERS均匀整理的$σ$，通过显示$ 1 <p <\ infty $和$ f \ in l^{p}（σ）$， \ [ \ lvert f \ rvert_ {l^{p}（σ）} \ sim \ left \ left \ lvert \ left（\ int_ {0}^{\ infty} \ left（α__{fσ}}（fσ}（x，x，x，x，r） \ frac {dr} {r} \ right）^{\ frac {1} {2}}} \ right \ rvert_ {l^{p}（p}（σ）}。 \]
We give a characterization of $L^{p}(σ)$ for uniformly rectifiable measures $σ$ using Tolsa's $α$-numbers, by showing, for $1<p<\infty$ and $f\in L^{p}(σ)$, that \[ \lVert f\rVert_{L^{p}(σ)}\sim \left\lVert\left(\int_{0}^{\infty} \left(α_{fσ}(x,r)+|f|_{x,r}α_σ(x,r)\right)^2\ \frac{dr}{r} \right)^{\frac{1}{2}}\right\rVert_{L^{p}(σ)}. \]
