Campanato spaces via quantum semigroups
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.
Related
- A note on the boundedness of the multidimensional Katugampola operator in Campanato spaces
- Optimal Embeddings of Campanato and Morrey Spaces
- Weak and Strong Convergence of an Implicit Iteration for Hemi-Contractive Semigroups in Banach Spaces
- a-numbers of covers in characteristic two: semigroups and Riemann-Roch spaces
- Composition Semigroups on the Besov Spaces
BibTeX
@misc{hong2026campanato,
title = {{Campanato spaces via quantum semigroups}},
author = {Guixiang Hong and Yuanyuan Jing and Ping Li},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22898},
eprint = {2609.22898},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22898},
}
RIS
TY - UNPB
TI - Campanato spaces via quantum semigroups
AU - Guixiang Hong
AU - Yuanyuan Jing
AU - Ping Li
PY - 2026
DA - 2026/09/19
PB - arXiv
DO - 10.48550/arxiv.2609.22898
UR - https://arxiv.org/abs/2609.22898
AB - 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.
ER -