{
  "abstract": "Let $λ>-1/2,\\neq0$. Consider the Bessel operators \\begin{align*} Δ_λ:=-\\frac{d^2}{dx^2}-\\frac{2λ}{x}\\frac{d}{dx} \\end{align*} on $\\mathbb{R}_+$. In this paper, we first establish several characterizations for $\\widetilde{A}_{\\infty,λ}$ weights introduced by Li et al. (Math. Z. 309(1) (2025), Paper No. 13, 29pp), which are different from the previous $A_p$ class with respect to the measure $x^{2λ}dx$. Among these characterizations, we obtain the sharp reverse Hölder inequality (RHI) for $\\widetilde{A}_{\\infty,λ}$ weights. As applications of RHI, we derive a precise open property of $\\widetilde{A}_{p,λ}$ weights, and obtain a sharp weighted bounds for the Hardy-Littlewood maximal operator $\\mathcal{M}_λ$ associated to $Δ_λ$, which was missing in the previous papers. Next, we also establish several extrapolation theorems related to $\\widetilde{A}_{p,λ}$ weights. Furthermore, we characterize the restricted weighted weak type estimates for $\\mathcal{M}_λ$ via a new class of weights $\\widetilde{A}_{p,λ}^{\\mathcal{R}}$, which is strictly larger than $\\widetilde{A}_{p,λ}$. Meanwhile, we obtain quantitative restricted weighted weak type $(p,p)$ bounds for sparse operators. As applications, we derive various kinds of weighted inequalities for Riesz transforms, maximal operators, square functions, variation operators and their commutators associated to $Δ_λ$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15260",
  "author_total": 2,
  "authors": [
    {
      "name": "Yongming Wen"
    },
    {
      "name": "Huoxiong Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f1d1kspp25rem.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15260",
  "fulltext_url": null,
  "id": "f1d1kspp25rem",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15260",
  "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.CA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7221768320",
  "pdf_url": "https://arxiv.org/pdf/2610.15260",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f1d1kspp25rem.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15260",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15260"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Weighted norm inequalities for operators with new Muckenhoupt type weights in the Bessel setting and applications",
  "title_text": "Weighted norm inequalities for operators with new Muckenhoupt type weights in the Bessel setting and applications",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/f1d1kspp25rem",
  "venue": "arXiv",
  "versions": []
}