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On higher order Morrey's inequalities over CD{\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 CD(K,N)-spaces for K∈ℝ and N∈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 H2, p(X) spaces on RCD(K, N)-spaces.

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Cite

BibTeXRIS
BibTeX
@misc{kitagawa2026higher,
  title = {{On higher order Morrey's inequalities over CD\boldmath$(K,N)$-spaces}},
  author = {Jun Kitagawa and Kazuhiro Kuwae},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2605.24404},
  eprint = {2605.24404},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.24404},
}
RIS
TY  - UNPB
TI  - On higher order Morrey's inequalities over CD{\boldmath(K,N)}-spaces
AU  - Jun Kitagawa
AU  - Kazuhiro Kuwae
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2605.24404
UR  - https://arxiv.org/abs/2605.24404
AB  - In this paper, we establish a higher order Morrey's inequality in the framework of CD(K,N)-spaces for K∈ℝ and N∈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 RCD(K, N)-spaces.
ER  -