{"paper":{"title":"A note on the off-diagonal Muckenhoupt-Wheeden conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Carlos P\\'erez, David Cruz-Uribe, Jos\\'e Mar\\'ia Martell","submitted_at":"2012-03-27T09:33:03Z","abstract_excerpt":"We obtain the off-diagonal Muckenhoupt-Wheeden conjecture for Calder\\'on-Zygmund operators. Namely, given $1<p<q<\\infty$ and a pair of weights $(u,v)$, if the Hardy-Littlewood maximal function satisfies the following two weight inequalities: $$ M : L^p(v) \\rightarrow L^q(u) \\quad \\text{and} \\quad M: L^{q'}(u^{1-q'}) \\rightarrow L^{p'}(v^{1-p'}), $$ then any Calder\\'on-Zygmund operator $T$ and its associated truncated maximal operator $T_\\star$ are bounded from $L^p(v)$ to $L^q(u)$. Additionally, assuming only the second estimate for $M$ then $T$ and $T_\\star$ map continuously $L^p(v)$ into $L^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.5906","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"}