{"paper":{"title":"$A_1$ theory of weights for rough homogeneous singular integrals and commutators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"C. Perez, I. Rivera-Rios, L. Roncal","submitted_at":"2016-07-21T19:07:27Z","abstract_excerpt":"Quantitative $A_1-A_\\infty$ estimates for rough homogeneous singular integrals $T_{\\Omega}$ and commutators of $BMO$ symbols and $T_{\\Omega}$ are obtained. In particular the following estimates are proved: %\n\\[ \\|T_\\Omega \\|_{L^p(w)}\\le c_{n,p}\\|\\Omega\\|_{L^\\infty} [w]_{A_1}^{\\frac{1}{p}}\\,[w]_{A_{\\infty}}^{1+\\frac{1}{p'}}\\|f\\|_{L^p(w)} \\] %\nand %\n\\[ \\| [b,T_{\\Omega}]f\\|_{L^{p}(w)}\\leq c_{n,p}\\|b\\|_{BMO}\\|\\Omega\\|_{L^{\\infty}} [w]_{A_1}^{\\frac{1}{p}}[w]_{A_{\\infty}}^{2+\\frac{1}{p'}}\\|f\\|_{L^{p}\\left(w\\right)}, \\] %\nfor $1<p<\\infty$ and $1/p+1/p'=1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06432","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"}