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PreprintCC BY-NC-ND 4.0arXiv

On Ck convex variants of Stein's Weighted L2 Conjecture for Bochner-Riesz means

  • Ruixiang Zhang
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Abstract

We prove power-loss results for some variants of Stein's Weighted L2 Conjecture for Bochner-Riesz means. The variants concern multipliers by convex bodies with Ck boundaries in every dimension n. The counterexamples are related to recently-constructed counterexamples to the Mizohata-Takeuchi Conjecture. Related results like logarithmic blowups for the endpoint case of the original conjecture are also discussed.

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Cite

BibTeXRIS
BibTeX
@misc{zhang2026convex,
  title = {{On $C^k$ convex variants of Stein's Weighted $L^2$ Conjecture for Bochner-Riesz means}},
  author = {Ruixiang Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.27045},
  eprint = {2609.27045},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.27045},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - On C^k convex variants of Stein's Weighted L^2 Conjecture for Bochner-Riesz means
AU  - Ruixiang Zhang
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.27045
UR  - https://arxiv.org/abs/2609.27045
AB  - We prove power-loss results for some variants of Stein's Weighted L^2 Conjecture for Bochner-Riesz means. The variants concern multipliers by convex bodies with C^k boundaries in every dimension n. The counterexamples are related to recently-constructed counterexamples to the Mizohata-Takeuchi Conjecture. Related results like logarithmic blowups for the endpoint case of the original conjecture are also discussed.
ER  -