{"paper":{"title":"Wavelets, Multiplier spaces and application to Schr\\\"{o}dinger type operators with non-smooth potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Pengtao Li, Qixiang Yang, Yueping Zhu","submitted_at":"2013-01-04T10:24:40Z","abstract_excerpt":"In this paper, we employ Meyer wavelets to characterize multiplier spaces between Sobolev spaces without using capacity. Further, we introduce logarithmic Morrey spaces $M^{t,\\tau}_{r,p}(\\mathbb{R}^{n})$ to establish the inclusion relation between Morrey spaces and multiplier spaces. By wavelet characterization and fractal skills, we construct a counterexample to show that the scope of the index $\\tau$ of $M^{t,\\tau}_{r,p}(\\mathbb{R}^{n})$ is sharp. As an application, we consider a Schr\\\"odinger type operator with potentials in $M^{t,\\tau}_{r,p}(\\mathbb{R}^{n})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0696","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"}