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arXiv · 2609.22898

Campanato spaces via quantum semigroups

Guixiang Hong·Yuanyuan Jing·Ping Li
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Abstract

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.

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Guixiang Hong, Yuanyuan Jing, Ping Li. 2026-09-19. Campanato spaces via quantum semigroups. https://arxiv.org/abs/2609.22898

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