{
  "abstract": "We prove mixed $A_p$-$A_\\infty$ estimates for sparse operators in two non-doubling settings. In the first setting, we consider sparse operators defined using stopping times in continuous time. We obtain both strong- and weak-type bounds with the same powers of the weight characteristics as in the classical setting. Some of our weak-type bounds are even new for the dyadic filtration on $\\mathbb R^d$ and, in particular, imply a sharp weak-type $(2,2)$ estimate for Rubio de Francia square functions, solving a problem left open by Garg, Roncal and Shrivastava [J. Geom. Anal., 31:748-771, 2021]. In the second setting, we consider dyadic sparse forms in which distinct cubes may interact, provided their dyadic distance is bounded. We obtain strong-type bounds with the same powers of the weight characteristics as in the classical setting. As a one-dimensional application, we obtain strong-type bounds for Haar shifts over balanced non-doubling measures, answering a quantitative question posed by Conde-Alonso, Pipher, and Wagner [Math. Ann., 391:2209-2253, 2025].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20531",
  "author_total": 2,
  "authors": [
    {
      "name": "Francisco Gonçalves"
    },
    {
      "name": "Emiel Lorist"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/avjbp6gmg1wqf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20531",
  "fulltext_url": null,
  "id": "avjbp6gmg1wqf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20531",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7213605002",
  "pdf_url": "https://arxiv.org/pdf/2609.20531",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/avjbp6gmg1wqf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20531",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20531"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp mixed $A_p$-$A_\\infty$ estimates for sparse operators on filtered and nonhomogeneous measure spaces",
  "title_text": "Sharp mixed A_p-A_∞ estimates for sparse operators on filtered and nonhomogeneous measure spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/avjbp6gmg1wqf",
  "venue": "arXiv",
  "versions": []
}