{"paper":{"title":"Two Weight Inequalities for Riesz Transforms: Uniformly Full Dimension Weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Brett D. Wick, Michael T. Lacey","submitted_at":"2013-12-20T22:03:47Z","abstract_excerpt":"Fix an integer $ n$ and number $d$, $ 0< d\\neq n-1 \\leq n$, and two weights $ w$ and $ \\sigma $ on $ \\mathbb R ^{n}$. We two extra conditions (1) no common point masses and (2) the two weights separately are not concentrated on a set of codimension one, uniformly over locations and scales. (This condition holds for doubling weights.) Then, we characterize the two weight inequality for the $ d$-dimensional Riesz transform on $ \\mathbb R ^{n}$, \\begin{equation*} \\sup_{0< a < b < \\infty}\\left\\lVert \\int_{a < \\lvert x-y\\rvert < b} f (y) \\frac {x-y} {\\lvert x-y\\rvert ^{d+1}} \\; \\sigma (dy) \\right\\r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6163","kind":"arxiv","version":4},"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"}