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PreprintarXiv licencearXiv

Critical Caffarelli-Kohn-Nirenberg inequalities via nonlinear scaling argument

  • Megumi Sano
  • Yerkin Shaimerdenov
  • Hinako Sugimura
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Abstract

We show functional inequalities with logarithmic weights as a critical case of Caffarelli-Kohn-Nirenberg inequalities. Original CKN inequalities have polynomial weights and are shown via scaling argument. In this paper, we develop this argument into it for nonlinear scaling. Our inequalities are generalizations of critical Hardy type inequalities.

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Cite

BibTeXRIS
BibTeX
@misc{sano2026critical,
  title = {{Critical Caffarelli-Kohn-Nirenberg inequalities via nonlinear scaling argument}},
  author = {Megumi Sano and Yerkin Shaimerdenov and Hinako Sugimura},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.28038},
  eprint = {2609.28038},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28038},
}
RIS
TY  - UNPB
TI  - Critical Caffarelli-Kohn-Nirenberg inequalities via nonlinear scaling argument
AU  - Megumi Sano
AU  - Yerkin Shaimerdenov
AU  - Hinako Sugimura
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.28038
UR  - https://arxiv.org/abs/2609.28038
AB  - We show functional inequalities with logarithmic weights as a critical case of Caffarelli-Kohn-Nirenberg inequalities. Original CKN inequalities have polynomial weights and are shown via scaling argument. In this paper, we develop this argument into it for nonlinear scaling. Our inequalities are generalizations of critical Hardy type inequalities.
ER  -