{"paper":{"title":"Positive Toeplitz operators on pluriharmonic Fock space: Schatten class criteria and sharp norm comparisons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Sam Looi","submitted_at":"2026-08-13T17:59:28Z","abstract_excerpt":"Let $\\mu$ be a positive Borel measure on $\\C^n$. For every $0<p<\\infty$, we prove that the Toeplitz operator $T_\\mu^{\\mathrm{ph}}$ induced by $\\mu$ on pluriharmonic Fock space belongs to $\\Sp_p$ if and only if $z\\mapsto\\mu(B(z,r))$ belongs to $L^p(\\C^n)$ for one, or equivalently every, $r>0$; this is also equivalent to Schatten membership of the corresponding holomorphic Toeplitz operator $T_\\mu$. For $n\\geq2$, this settles a conjecture of Jaguzovi\\'c and Vujadinovi\\'c, and the result includes the range $0<p<1$ in every dimension. Moreover, \\[\n  \\norm{T_\\mu}_{\\Sp_p}^p\n  \\leq\\norm{T_\\mu^{\\mathr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.13550","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.13550/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}