{
  "abstract": "In this paper, we establish a new version of one dimensional generalized discrete dual $p$-Hardy inequality with a shift. Using this generalized discrete dual p-Hardy inequality, we obtain improvements of two discrete dual $p$-Hardy inequalities. To be specific, for $p>1$ and $A\\in C_c(\\mathbb{N}_{0})$ satisfying $A_{0}=A_{1}=0$, we first improve the discrete dual p-Hardy inequality \\begin{align*} &\\displaystyle\\sum_{n=2}^{\\infty}(n-1)^{p}| A_{n}-A_{n-1}|^{p}\\geq\\frac{1}{p^{p}}\\displaystyle\\sum_{n=2}^{\\infty}|A_{n}|^{p}, \\end{align*} where the associate constant term is sharp. Subsequently, we improve its power-type weighted discrete dual p-Hardy extension \\begin{align*} &\\displaystyle\\sum_{n=2}^{\\infty}(n-1)^α|A_{n}-A_{n-1}|^{p}\\geq\\Big(\\frac{α+1-p}{p}\\Big)^{p} \\displaystyle\\sum_{n=2}^{\\infty}\\frac{|A_{n}|^{p}}{n^{p-α}} \\end{align*} for $p-1<α\\leq p$, where the associated constant term is also sharp. We also establish a discrete $p$- Birman inequality with power weights. Furthermore, we establish a multivariable dual $p$-Hardy inequality with a sharp constant. The proof proceeds by first establishing the inequality for two variables and then extending the argument to multiple variables, while preserving the sharpness of the constant.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11890",
  "author_total": 1,
  "authors": [
    {
      "name": "Bikram Das"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fggk36j9n3wet.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11890",
  "fulltext_url": null,
  "id": "fggk36j9n3wet",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11890",
  "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|Mathematical Inequalities and Applications"
    ]
  ],
  "openalex": "W7212260949",
  "pdf_url": "https://arxiv.org/pdf/2609.11890",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fggk36j9n3wet.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11890",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11890"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Improved Discrete Dual $p$-Hardy and Weighted Discrete $p$- Birman Inequalities",
  "title_text": "Improved Discrete Dual p-Hardy and Weighted Discrete p- Birman Inequalities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/fggk36j9n3wet",
  "venue": "arXiv",
  "versions": []
}