{"paper":{"title":"L^p(R^n)-continuity of translation invariant anisotropic pseudodifferential operators: a necessary condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"M. Murdocca, S. Coriasco","submitted_at":"2012-10-02T07:56:12Z","abstract_excerpt":"We consider certain anisotropic translation invariant pseudodifferential operators, belonging to a class denoted by $\\mathrm{op}(\\mathcal{M}^{\\lambda}_{\\psi})$, where $\\lambda$ and $\\psi=(\\psi_1,\\dots,\\psi_n)$ are the \"order\" and \"weight\" functions, defined on $\\mathbb{R}^n$, for the corresponding space of symbols. We prove that the boundedness of a suitable function $F_p\\colon\\mathbb{R}^n\\to[0,+\\infty)$, $1<p<\\infty$, associated with $\\lambda$ and $\\psi$, is necessary to let every element of $\\mathrm{op}(\\mathcal{M}^{\\lambda}_{\\psi})$ be a $L^p(\\mathbb{R}^n)$-multiplier. Additionally, we show"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0694","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}