{
  "abstract": "Suppose that $([0,1],\\mathcal{A},μ)$ is the Lebesgue measure space and $1< p<\\infty$ with $\\frac{1}{p}+\\frac{1}{q}=1$. We prove that an unit vector $h\\in L^{p}(μ, X)^*$ is a weak$^*$-weak point of continuity of $S(L^{p}(μ, X)^*)$ if and only if $\\frac{h(t)}{\\|h(t)\\|}$ is a weak$^*$-weak point of continuity of $S(X^*)$ for almost every $t\\in [0, 1]$ with $h(t)\\neq 0$, where $X$ is a Banach space such that $X^*$ is separable. As an application of this result, under the same hypothesis on $X$, we prove that a point $f\\in L^p(μ, X)_{1}$ is a very smooth point if and only if $\\frac{f(t)}{\\|f(t)\\|}\\in S(X)$ is a very smooth point for almost every $t\\in [0, 1]$ with $f(t)\\neq 0$. We give several examples to show that these results does not hold for $p=1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23502",
  "author_total": 1,
  "authors": [
    {
      "name": "Saurabh Dwivedi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2nrvazjd0skg8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23502",
  "fulltext_url": null,
  "id": "2nrvazjd0skg8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23502",
  "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",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7222959053",
  "pdf_url": "https://arxiv.org/pdf/2610.23502",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2nrvazjd0skg8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23502",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23502"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Weak$^*$-weak points of continuity and very smooth points in Bochner function spaces $L^{p}(μ, X)$",
  "title_text": "Weak^*-weak points of continuity and very smooth points in Bochner function spaces L^p(μ, X)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/2nrvazjd0skg8",
  "venue": "arXiv",
  "versions": []
}