{"paper":{"title":"Mixed weak estimates of Sawyer type for fractional integrals and some related operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fabio Berra, Gladis Pradolini, Marilina Carena","submitted_at":"2017-12-21T19:31:48Z","abstract_excerpt":"We prove mixed weak estimates of Sawyer type for fractional operators. More precisely, let $\\mathcal{T}$ be either the maximal fractional function $M_\\gamma$ or the fractional integral operator $I_\\gamma$, $0<\\gamma<n$, $1\\leq p<n/\\gamma$ and $1/q=1/p-\\gamma/n$. If $u,v^{q/p}\\in A_1$ or if $uv^{-q/{p'}}\\in A_1$ and $v^q\\in A_\\infty(uv^{-q/{p'}})$ then we obtain that the estimate \\begin{equation*} uv^{q/p}\\left(\\left\\{x\\in \\R^n: \\frac{|\\mathcal{T}(fv)(x)|}{v(x)}>t\\right\\}\\right)^{1/q}\\leq \\frac{C}{t}\\left(\\int_{\\R^n}|f(x)|^pu(x)^{p/q}v(x)\\,dx\\right)^{1/p}, \\end{equation*} holds for every positi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.08186","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"}