{
  "abstract": "We establish a necessary and sufficient weight condition so that a modular inequality holds for a generalized integral operator $T_ϕ$ on non-negative non-increasing functions in weighted variable Lebesgue spaces $L_w^{p(x)}.$ We give a condition under which the mentioned modular inequality leads to a norm inequality. Lastly, examples are given to demonstrate our main result, to obtain modular inequalities for some well known operators.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09029",
  "author_total": 2,
  "authors": [
    {
      "name": "Megha Madan"
    },
    {
      "name": "Arun Pal Singh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/614m5ze3g0dr8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09029",
  "fulltext_url": null,
  "id": "614m5ze3g0dr8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09029",
  "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|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7212050597",
  "pdf_url": "https://arxiv.org/pdf/2609.09029",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/614m5ze3g0dr8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:01Z",
      "native_id": "2609.09029",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09029"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Some weighted modular inequalities in variable Lebesgue spaces",
  "title_text": "Some weighted modular inequalities in variable Lebesgue spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:01Z",
  "url": "https://research.draconitic.com/paper/614m5ze3g0dr8",
  "venue": "arXiv",
  "versions": []
}