{"paper":{"title":"Fourth-order Schr\\\"odinger type operator with singular potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Federica Gregorio, Sebastian Mildner","submitted_at":"2016-01-20T11:47:05Z","abstract_excerpt":"In this paper we study the biharmonic operator perturbed by an inverse fourth-order potential. In particular, we consider the operator $A=\\Delta^2-V=\\Delta^2-c|x|^{-4}$ where $c$ is any constant such that $c<\\left(\\frac{N(N-4)}{4}\\right)^2$. The semigroup generated by $-A$ in $L^2(\\mathbb{R}^N)$, $N\\geq5$, extrapolates to a bounded holomorphic $C_0$-semigroup on $L^p(\\mathbb{R}^N)$ for $p\\in [p^{'}_0,p_0]$ where $p_0=\\frac{2N}{N-4}$ and $p_0^{'}$ is its dual exponent. Furthermore, we study the boundedness of the Riesz transform $\\Delta A^{-1/2}$ on $L^p(\\mathbb{R}^N)$ for all $p\\in(p_0^{'},2]$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05243","kind":"arxiv","version":2},"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"}