卷积Calderón--Zygmund算子的Morrey到Lebesgue等价性

中文摘要 AI 辅助

我们证明，对于向量值的卷积Calderón--Zygmund算子，在单个非平凡Morrey空间上的有界性等价于相应的全局$L^p$有界性。因此，一个Morrey尺度已经包含了所有有限$p$的有界性信息。从Morrey到$L^p$的蕴含通过一个分离副本放大论证获得，该论证从单个尺度局部估计重构全局范数；逆命题在相同的向量值框架下通过局部/远场分解证明。作为推论，向量值Hilbert变换在单个非平凡Morrey空间上的有界性等价于UMD性质。结果表明，Morrey估计并未绕过经典的Banach空间障碍：它们恰好检测到该障碍。

英文摘要

We prove that, for vector-valued convolution Calderón--Zygmund operators, boundedness on a single nontrivial Morrey space is equivalent to the corresponding global $L^p$ boundedness. Thus one Morrey scale already contains the full finite-$p$ boundedness information. The implication from Morrey to $L^p$ is obtained by a separated-copy amplification argument that reconstructs the global norm from a single scale-local estimate; the converse is proved in the same vector-valued framework by a local/far-field decomposition. As a consequence, boundedness of the vector-valued Hilbert transform on one nontrivial Morrey space is equivalent to the UMD property. The result shows that Morrey estimates do not bypass the classical Banach-space obstruction: they detect it exactly.

发表机构

• Cellular Products Research and Development（细胞产品研发部）
• Antalya Bilim University（安塔利亚科技大学）

机构由 AI 辅助整理，请以论文原文为准。