{"paper":{"title":"On two-weight norm inequalities for positive dyadic operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Igor E. Verbitsky, Timo S. H\\\"anninen","submitted_at":"2018-09-27T23:37:58Z","abstract_excerpt":"Let $\\sigma$ and $\\omega$ be locally finite Borel measures on $\\mathbb{R}^d$, and let $p\\in(1,\\infty)$ and $q\\in(0,\\infty)$. We study the two-weight norm inequality $$ \\lVert T(f\\sigma) \\rVert_{L^q(\\omega)}\\leq C \\lVert f \\rVert_{L^p(\\sigma)}, \\quad \\text{for all} \\, \\, f \\in L^p(\\sigma), $$ for both the positive summation operators $T=T_\\lambda(\\cdot \\sigma)$ and positive maximal operators $T=M_\\lambda(\\cdot \\sigma)$. Here, for a family $\\{\\lambda_Q\\}$ of non-negative reals indexed by the dyadic cubes $Q$, these operators are defined by $$ T_\\lambda(f\\sigma):=\\sum_Q \\lambda_Q \\langle f\\rangle"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10800","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"}