{
  "abstract": "Aleman, Olsen, and Saksman asked whether radial convergence may fail for bounded analytic functions on the infinite-dimensional polydisc when every radial point has non-increasing coordinates, and whether the approach may be chosen independently of the boundary point. We construct a point-dependent counterexample in which every fixed coordinate nevertheless increases to $1$. A finite discretization yields a boundary-point-independent coordinatewise decreasing approach for which convergence to the boundary function fails almost everywhere. In contrast, every boundary-point-independent approach whose fixed coordinates increase monotonically to $1$ satisfies an $L^p$ maximal inequality and the almost-everywhere Fatou theorem for $1<p<\\infty$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.03164",
  "author_total": 3,
  "authors": [
    {
      "name": "Jiawei Sun"
    },
    {
      "name": "Chao Zu"
    },
    {
      "name": "Yufeng Lu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3w9z4a34kz940.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.03164",
  "fulltext_url": null,
  "id": "3w9z4a34kz940",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.03164",
  "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.FA"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7172483256",
  "pdf_url": "https://arxiv.org/pdf/2608.03164",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3w9z4a34kz940.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:57Z",
      "native_id": "2608.03164",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.03164"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Radial Convergence along Decreasing Coordinate Radii in \\texorpdfstring{$H^\\infty(\\T^\\infty)$}{H-infinity(T-infinity)}",
  "title_text": "Radial Convergence along Decreasing Coordinate Radii in \\texorpdfstring{H^∞(T^∞)}{H-infinity(T-infinity)}",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:57Z",
  "url": "https://research.draconitic.com/paper/3w9z4a34kz940",
  "venue": "arXiv",
  "versions": []
}