{"paper":{"title":"Multipliers and imaginary powers of the schr\\\"odinger operators characterizing UMD Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"And L. Rodr\\'Iguez-Mesa, J.C. Fari\\~na, J.J. Betancor, R. Crescimbeni","submitted_at":"2011-09-02T12:41:00Z","abstract_excerpt":"In this paper we establish $L^p$-boundedness properties for Laplace type transform spectral multipliers associated with the Schr\\\"odinger operator $\\mathcal{L}=-\\Delta +V$. We obtain for this type of multipliers pointwise representation as principal value integral operators. We also characterize the UMD Banach spaces in terms of the $L^p$-boundedness of the imaginary powers $\\mathcal{L}^{i\\gamma}$, $\\gamma \\in \\mathbb{R}$, of $\\mathcal{L}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0429","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":""},"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"}