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Orthonormal maximal estimates for fractional Schrödinger operators along Hölder curves

  • Eunhee Jeong
  • Hyerim Ko
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Abstract

We establish orthonormal maximal estimates for one-dimensional fractional Schrödinger operators along curves that are Hölder continuous in time and bi-Lipschitz in space. For both the convex range m>1 and the concave range 0<m<1, we obtain sharp Sobolev regularity in terms of the order m. As an application, we obtain almost everywhere convergence of the associated densities to their initial values along the curves. The proof combines Schatten duality with kernel estimates.

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Cite

BibTeXRIS
BibTeX
@misc{jeong2026orthonormal,
  title = {{Orthonormal maximal estimates for fractional Schrödinger operators along Hölder curves}},
  author = {Eunhee Jeong and Hyerim Ko},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.23576},
  eprint = {2610.23576},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.23576},
}
RIS
TY  - UNPB
TI  - Orthonormal maximal estimates for fractional Schrödinger operators along Hölder curves
AU  - Eunhee Jeong
AU  - Hyerim Ko
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2610.23576
UR  - https://arxiv.org/abs/2610.23576
AB  - We establish orthonormal maximal estimates for one-dimensional fractional Schrödinger operators along curves that are Hölder continuous in time and bi-Lipschitz in space. For both the convex range m>1 and the concave range 0<m<1, we obtain sharp Sobolev regularity in terms of the order m. As an application, we obtain almost everywhere convergence of the associated densities to their initial values along the curves. The proof combines Schatten duality with kernel estimates.
ER  -