Year: 2026
Type: preprint
Abstract: In this paper, we establish a higher order Morrey's inequality in the framework of $\mathsf{CD}(K,N)$-spaces for $K\in\mathbb{R}$ and $N\in\mathbb{N}$. We do so by first introducing an alternate version of second order Sobolev spaces in general metric measure spaces, which contains amply many functions even when $p>N$. These spaces contain the traditional $H^{2, p}(X)$ spaces on $\mathsf{RCD}(K, N)$-spaces.
Source: arXiv (Cornell University)
Authors: Kitagawa, Jun, Kuwae, Kazuhiro
Institutions: Michigan State University, Fukuoka University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7162393685