{
  "abstract": "We study Strichartz estimates for orthonormal families of initial data when time is integrated against an $α$-dimensional Frostman measure $μ$, $0<α\\le1$, with coefficients measured in $\\ell^β$. For the fractional Schrödinger, wave and Klein--Gordon equations, we obtain orthogonality gains in the admissible region and necessary conditions on $β$. For the fractional Schrödinger equation the exponents are sharp up to an endpoint; the optimality of the threshold $β=q/2$ requires $μ$ to be Ahlfors regular. For the Schrödinger equation in dimensions $d\\ge2$, we prove a Lorentz endpoint estimate and, if $d>2α$, the critical exponent $β=q/2$ at every pair $2\\le q,r<\\infty$ with \\[\\frac d2(\\frac12-\\frac1r)\\ge\\fracαq, \\quad r>\\frac{dq}{d-α};\\] on $r=\\infty$ we obtain a restricted weak-type estimate. Since the constants depend on $μ$ only through its Frostman constant, Lebesgue measure yields global-in-time critical estimates in this range when $d\\ge3$. The proofs combine Frostman fractional integration, a spectral near--far argument at the endpoint, and asymmetric Hilbert--Schmidt bounds with orthogonal frequency-block summation. We also obtain further estimates in the low-dimensional cases $d=1$ (fractional Schrödinger) and $d=2$ (wave and Klein--Gordon) with $α>1/2$, and formulate the consequences for densities of freely evolving states.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18042",
  "author_total": 3,
  "authors": [
    {
      "name": "Guoxia Feng"
    },
    {
      "name": "Jinbong Lee"
    },
    {
      "name": "Sanghyuk Lee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/56zpgb06j77g3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18042",
  "fulltext_url": null,
  "id": "56zpgb06j77g3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18042",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7221784677",
  "pdf_url": "https://arxiv.org/pdf/2610.18042",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/56zpgb06j77g3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.18042",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18042"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Orthonormal Strichartz estimates over fractal time",
  "title_text": "Orthonormal Strichartz estimates over fractal time",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/56zpgb06j77g3",
  "venue": "arXiv",
  "versions": []
}