{
  "abstract": "In this paper, we study $L^p$-estimates for maximal averaging operators $\\mathcal M$ along hypersurfaces $S$ in $\\mathbb{R}^{3}$ which are the graph of a mixed homogeneous function $Φ$ which is analytic away from the origin. The closure of such a surface will pass through the origin, so that the usual transversality condition that had been imposed in many previous works on maximal averages along hypersurfaces will not hold even when $Φ$ is analytic at the origin. As our main result, under mild assumptions which are satisfied for instance for every mixed homogeneous polynomial $Φ,$ we determine the critical Lebesgue exponent $p_c$ for which $\\mathcal M$ is $L^p$-bounded for every $p>p_c,$ but unbounded for $p<p_c,$ in terms of multiplicities of the real roots of the Hessian determinant of $Φ.$ It turns out that the study of the contributions by neighborhoods of a certain type of roots is closely related to recent work by Dendrinos, Ikromov and the first and third author on sharp estimates for a maximal averaging operator along a transversal hypersurface of an ``exceptional'' class, whose $L^p$-boundedness had been an open problem for a long time and which has recently been established by means of their new theory of FIO-cone multipliers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.22012",
  "author_total": 4,
  "authors": [
    {
      "name": "Stefan Buschenhenke"
    },
    {
      "name": "Wenjuan Li"
    },
    {
      "name": "Detlef Müller"
    },
    {
      "name": "Huiju Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2bqgr36mvck3r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.22012",
  "fulltext_url": null,
  "id": "2bqgr36mvck3r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.22012",
  "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.CA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7204210332",
  "pdf_url": "https://arxiv.org/pdf/2608.22012",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2bqgr36mvck3r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2608.22012",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.22012"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "$L^p$-Estimates for maximal averages along mixed homogeneous hypersurfaces in $\\mathbb{R}^{3}$",
  "title_text": "L^p-Estimates for maximal averages along mixed homogeneous hypersurfaces in ℝ^3",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/2bqgr36mvck3r",
  "venue": "arXiv",
  "versions": []
}