{
  "abstract": "We study logarithmic Hardy operators and their commutators on the half-line Morrey spaces defined using all bounded intervals. For 1≤p<∞, 0<λ<1, and γ>−1, the positive dilation principle gives the exact norm Γ(γ+1)[p/(p+λ−1)]γ+1, attained by a power function. We obtain exact norms for Hardy iterates and a reverse inequality for nonnegative nonincreasing functions. For the fractional operator, we prove a mapping theorem between distinct Morrey spaces, establish the necessary scaling relation, and give explicit upper bounds throughout a logarithmic range that is optimal for finiteness at every point. We distinguish this pointwise threshold from the almost-everywhere mapping endpoint. For the one-sided point-value symbol class, we prove embeddings into ordinary and central mean-oscillation spaces and identify its relation to the symmetric point-value class through even extension. This symbol condition yields explicit logarithmic and fractional commutator estimates. The symbol b(x)=logx raises the logarithmic order by one and gives an exact commutator norm with which the general upper bound can be compared.",
  "abstract_shown": true,
  "affiliations": [
    "Departamento de Matemática y Estadística, Universidad Nacional Pedro Henríquez Ureña, Santo Domingo 1423, Dominican Republic",
    "Instituto de Matemática, Facultad de Ciencias, Universidad Autónoma de Santo Domingo, Santo Domingo 1356, Dominican Republic"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0,
        1
      ],
      "name": "Francis Mora-Ferreras"
    },
    {
      "affs": [
        1
      ],
      "name": "Manuel Montero"
    },
    {
      "affs": [
        1
      ],
      "name": "Victor Ramírez"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/az7vy328kqj15.bib",
  "cited_by": 0,
  "doi": "10.3390/math14203824",
  "fulltext_url": null,
  "id": "az7vy328kqj15",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/20/3824",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7223134332",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/az7vy328kqj15.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14203824",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/20/3824"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2604|Advanced Harmonic Analysis Research",
      "subfield": "general"
    }
  ],
  "title": "Exact Norms and Morrey Estimates for Logarithmic Hardy Operators and Their Commutators on the Half-Line",
  "title_text": "Exact Norms and Morrey Estimates for Logarithmic Hardy Operators and Their Commutators on the Half-Line",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/az7vy328kqj15",
  "venue": "Mathematics",
  "versions": []
}