发表机构
Institute for Advanced Study in Mathematics, Harbin Institute of Technology; Wuhan University of Science and Technology（哈尔滨工业大学数学高等研究院; 武汉科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究von Neumann代数上半群的Campanato空间，证明其与Lipschitz空间对所有正指标及解析半群重合，并验证自改进性质，进而推出列与行空间同构，推广了先前工作。
AI 中文摘要
本文继续研究von Neumann代数上半群上的Campanato空间。主要结果之一是：对于所有正则指标$\alpha > 0$以及von Neumann代数上所有解析半群（不必是有限的），Campanato空间与Lipschitz空间重合；同时验证了Campanato空间所期望的自改进性质。作为推论，我们证明了对于所有$\alpha > 0$，列Campanato空间与行Campanato空间同构。这不仅去除了前两位作者先前工作\cite{HJ24}中的若干限制，还将先前结果推广到任意解析半群，从而解决了\cite{HJ24}中遗留的几个问题。即使在交换情形下，这些结果和证明也是全新的。
英文摘要
In this paper, we continue to investigate Campanato spaces via semigroups on von Neumann algebras. One of the main results is their coincidence with Lipschitz spaces for {\it all} regularity indices $α> 0$ and for all {\it analytic} semigroups on von Neumann algebras {\it not necessarily being finite}; the desired self-improving property of Campanato spaces has also been verified. As a consequence, we demonstrate that the column Campanato spaces are isomorphic to the row ones for {\it all} $α> 0$. This not only removes several restrictions in the previous work \cite{HJ24} by the first two authors, but also extends the previous results to any analytic semigroup, and thus resolves several problems left open in \cite{HJ24}. Both the results and the proof are new even in the commutative setting.
