{
  "abstract": "We study weighted and Sobolev estimates for two fractional Schrödinger operators on $\\mathbb{R}^n$, where $n\\geq3$ and $0<s<1$. For the additive operator $L=(-Δ)^s+V$, with a nonnegative, nontrivial potential $V$ belonging to a suitable reverse Hölder class, $RH_q$, we establish a critical-radius form inequality and decay estimates for the semigroup mass. These yield a heat-kernel bound combining polynomial off-diagonal decay with a fixed positive exponent of decay relative to the fractional critical radius $ρ_s$. A decomposition at this scale gives weighted strong-type estimates for the semigroup maximal operator and weighted Hardy--Littlewood--Sobolev estimates for $L^{-α/2}$, $0<αs<n$, together with the corresponding endpoint weak-type estimates. The admissible weights satisfy explicit growth restrictions determined by the kernel decay, and the fractional integration order is $αs$. We also consider the spectral operator $Q=(-Δ+V)^s$. Assuming $V\\in RH_{q_1}$ with $n/(1+s)\\leq q_1<n$ and classical critical radius $ρ_1(x)\\geq1$, we prove that $\\nabla Q^{-1/2}$ maps $H^{1-s,p}(\\mathbb{R}^n)$ into $L^p(\\mathbb{R}^n)$ for $1<p\\leq p_0$, where $1/p_0=1/q_1-1/n$. By duality, its adjoint maps $L^{p^{'}}(\\mathbb{R}^n)$ into $H^{s-1,p^{'}}(\\mathbb{R}^n)$ for $p_0^{'}\\leq p^{'}<\\infty$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16274",
  "author_total": 2,
  "authors": [
    {
      "name": "Aparajita Dasgupta"
    },
    {
      "name": "Drishti Garg"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9bv70x37y1hqa.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16274",
  "fulltext_url": null,
  "id": "9bv70x37y1hqa",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16274",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7221756644",
  "pdf_url": "https://arxiv.org/pdf/2610.16274",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9bv70x37y1hqa.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.16274",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16274"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Weighted and Sobolev Estimates for Fractional Schrödinger Operators with Reverse Hölder Potentials",
  "title_text": "Weighted and Sobolev Estimates for Fractional Schrödinger Operators with Reverse Hölder Potentials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/9bv70x37y1hqa",
  "venue": "arXiv",
  "versions": []
}