{"paper":{"title":"Two weight Commutators in the Dirichlet and Neumann Laplacian settings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Brett D. Wick, Dongyong Yang, Irina Holmes, Ji Li, Xuan Thinh Duong","submitted_at":"2017-05-19T04:38:25Z","abstract_excerpt":"In this paper we establish the characterization of the weighted BMO via two weight commutators in the settings of the Neumann Laplacian $\\Delta_{N_+}$ on the upper half space $\\mathbb{R}^n_+$ and the reflection Neumann Laplacian $\\Delta_N$ on $\\mathbb{R}^n$ with respect to the weights associated to $\\Delta_{N_+}$ and $\\Delta_{N}$ respectively. This in turn yields a weak factorization for the corresponding weighted Hardy spaces, where in particular, the weighted class associated to $\\Delta_{N}$ is strictly larger than the Muckenhoupt weighted class and contains non-doubling weights. In our stud"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06858","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"}