Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Hong, Guixiang, Jing, Yuanyuan, Li, Ping
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214029310