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arXiv · 2605.24404

On higher order Morrey's inequalities over RCD{\boldmath$(K,N)$}-spaces

Jun Kitagawa·Kazuhiro Kuwae
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Abstract

In this paper, we establish a higher order Morrey's inequality in the framework of %non-collapsed $\mathsf{RCD}(K,N)$-spaces for $K\in\mathbb{R}$ and $N\in\mathbb{N}$. We do so by first introducing an alternate version of the second order Sobolev space $W^{2, p}(X)$, which contains amply many functions even when $p>N$.

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Jun Kitagawa, Kazuhiro Kuwae. 2026-05-23. On higher order Morrey's inequalities over RCD{\boldmath$(K,N)$}-spaces. https://arxiv.org/abs/2605.24404

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