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PreprintarXiv licencearXiv

Endpoint bounds for the Born-Jordan distribution

  • Yaojun Wang
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Abstract

For dgeqslant3, let p*=2d/(d−2). We prove that the Born-Jordan distribution maps L2,p*(ℝd)× L2,p*(ℝd) boundedly into Lp*(ℝ2d). The Lorentz index p* cannot be increased in either variable. In particular, this gives the endpoint L2× L2→ Lp* estimate, settling the critical boundedness problem raised by Stra, Svela, and Trapasso \cite{SST26}.

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Cite

BibTeXRIS
BibTeX
@misc{wang2026endpoint,
  title = {{Endpoint bounds for the Born-Jordan distribution}},
  author = {Yaojun Wang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08922},
  eprint = {2609.08922},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.08922},
}
RIS
TY  - UNPB
TI  - Endpoint bounds for the Born-Jordan distribution
AU  - Yaojun Wang
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.08922
UR  - https://arxiv.org/abs/2609.08922
AB  - For dgeqslant3, let p^*=2d/(d−2). We prove that the Born-Jordan distribution maps L^2,p^*(ℝ^d)× L^2,p^*(ℝ^d) boundedly into L^p^*(ℝ^2d). The Lorentz index p^* cannot be increased in either variable. In particular, this gives the endpoint L^2× L^2→ L^p^* estimate, settling the critical boundedness problem raised by Stra, Svela, and Trapasso \cite{SST26}.
ER  -