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PreprintCC BY 4.0arXiv

Sharp L6 Fourier moments and (3,δ)-energy estimates for fractal measures on the truncated cone in R3

  • Ciprian Demeter
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Abstract

For a δ-separated (δ,d)-Katz--Tao set P on the truncated cone in R3, 1<d≤ 2, we prove the sharp energy bound E3,δ(P)≲ε δ−ε max{δ−(3d+2),δ−(5d−1)}. The proof applies the Fu--Ren incidence theorem to triples with a fixed sum. As a corollary we also deduce a sharp L6 moment estimate for the Fourier transform of Frostman measures supported on the cone.

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Cite

BibTeXRIS
BibTeX
@misc{demeter2026sharp,
  title = {{Sharp $L^6$ Fourier moments and (3,$δ$)-energy estimates for fractal measures on the truncated cone in $\R^3$}},
  author = {Ciprian Demeter},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.23679},
  eprint = {2610.23679},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.23679},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Sharp L^6 Fourier moments and (3,δ)-energy estimates for fractal measures on the truncated cone in R^3
AU  - Ciprian Demeter
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2610.23679
UR  - https://arxiv.org/abs/2610.23679
AB  - For a δ-separated (δ,d)-Katz--Tao set P on the truncated cone in R^3, 1<d≤ 2, we prove the sharp energy bound E_3,δ(P)≲_ε δ^−ε max{δ^−(3d+2),δ^−(5d−1)}. The proof applies the Fu--Ren incidence theorem to triples with a fixed sum. As a corollary we also deduce a sharp L^6 moment estimate for the Fourier transform of Frostman measures supported on the cone.
ER  -