{"paper":{"title":"$T1$ criterions for generalised Calder\\'on--Zygmund type operators on Hardy and BMO spaces associated to Schr\\\"odinger operators and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fu Ken Ly, Ji Li, The Anh Bui","submitted_at":"2015-10-09T00:01:27Z","abstract_excerpt":"Suppose $L=-\\Delta+V$ is a Schr\\\"odinger operator on $\\mathbb{R}^n$ with a potential $V$ belonging to certain reverse H\\\"older class $RH_\\sigma$ with $\\sigma\\geq n/2$. The main aim of this paper is to provide necessary and sufficient conditions in terms of $T1$ criteria for a generalised Calder\\'on--Zygmund type operator with respect to $L$ to be bounded on Hardy spaces $H^p_L(\\mathbb{R}^n)$ and on BMO type spaces BMO$_L^\\alpha(\\mathbb{R}^n)$ associated with $L$. As applications, we prove the boundedness for several singular integral operators associated to $L$. Our approach is flexible enough"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02531","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"}