{
  "abstract": "We study real interpolation of the $G$-measurable subspaces $Y_j$ of variable Lebesgue spaces $L^{p_j(\\cdot)}$. For a family of continuous exponent pairs that vary in opposite directions on the atoms of $G$, we prove that $K$-closedness is equivalent to a uniform logarithmic bound on the oscillation of the exponents. The same bound characterizes the existence of a common bounded projection and interpolation equality at a single interior parameter. If it fails, then for each $0<θ<1$ there is one function belonging to all ambient interpolation spaces $(X_0,X_1)_{θ,q}$, $0<q\\leq\\infty$, and to none of the corresponding spaces $(Y_0,Y_1)_{θ,q}$. Each endpoint subspace still admits a bounded positive projection. The exponents can be chosen arbitrarily close to prescribed constants $1<a<b<\\infty$, with constant sum and smoothness away from zero. We also give a finite-profile criterion in terms of the endpoint maxima, compute the associated $K$-functional loss, and obtain a counterexample for adapted sequence spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24904",
  "author_total": 1,
  "authors": [
    {
      "name": "Asad Ullah"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1k2tremf8m6pc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24904",
  "fulltext_url": null,
  "id": "1k2tremf8m6pc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24904",
  "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": "W7222994552",
  "pdf_url": "https://arxiv.org/pdf/2610.24904",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1k2tremf8m6pc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24904",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24904"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Opposed Exponent Profiles and Real Interpolation of Measurable Subspaces",
  "title_text": "Opposed Exponent Profiles and Real Interpolation of Measurable Subspaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/1k2tremf8m6pc",
  "venue": "arXiv",
  "versions": []
}