论文标题
$ l_p $ spaces之间的严格奇异非压缩操作员
Strictly singular non-compact operators between $L_p$ spaces
论文作者
论文摘要
我们研究了$ L_P $空间之间严格的奇异非压缩操作员的结构。回答[adv。数学。 316（2017），667-690]，显示出存在$ t $，其中一组点$（\ frac1p，\ frac1q）\ in（0,1）\ times \ times（0,1） $ \ {（\ frac1p，\ frac1q）：1 <p <q <q <\ infty \} $的任何正斜率。这将通过RIESZ潜在的操作员在具有不同Hausdorff维度的度量空间之间实现。还探索了在$ L_P $子空间上定义的常规运算符的紧凑性与严格的奇异性之间的关系。
We study the structure of strictly singular non-compact operators between $L_p$ spaces. Answering a question raised in [Adv. Math. 316 (2017), 667-690], it is shown that there exist operators $T$, for which the set of points $(\frac1p,\frac1q)\in(0,1)\times (0,1)$ such that $T:L_p\rightarrow L_q$ is strictly singular but not compact contains a line segment in the triangle $\{(\frac1p,\frac1q):1<p<q<\infty\}$ of any positive slope. This will be achieved by means of Riesz potential operators between metric measure spaces with different Hausdorff dimension. The relation between compactness and strict singularity of regular operators defined on subspaces of $L_p$ is also explored.
