{"paper":{"title":"Mixed weak estimates of Sawyer type for commutators of singular integrals and related operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Fabio Berra, Gladis Pradolini, Marilina Carena","submitted_at":"2017-04-17T13:10:57Z","abstract_excerpt":"We study mixed weak type inequalities for the commutator $[b,T]$, where $b$ is a BMO function and $T$ is a Calder\\'on-Zygmund operator. More precisely, we prove that for every $t>0$ \\begin{equation*}%\\label{tesis_teo2.2} uv(\\{x\\in\\R^n: |\\frac{[b,T](fv)(x)}{v(x)}|>t\\})\\leq C\\int_{\\R^n}\\phi(\\frac{|f(x)|}{t})u(x)v(x)\\,dx, \\end{equation*} where $\\phi(t)=t(1+\\log^{+}{t})$, $u\\in A_1$ and $v\\in A_{\\infty}(u)$. Our technique involves the classical Calder\\'on-Zygmund decomposition, which allow us to give a direct proof. We use this result to prove an analogous inequality for higher order commutators. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.04953","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"}