{"paper":{"title":"Non-homogeneous square functions on general sets: suppression and big pieces methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Emil Vuorinen, Henri Martikainen, Mihalis Mourgoglou","submitted_at":"2016-06-14T11:04:49Z","abstract_excerpt":"We aim to showcase the wide applicability and power of the big pieces and suppression methods in the theory of local $Tb$ theorems. The setting is new: we consider conical square functions with cones $\\{x \\in \\mathbb{R}^n \\setminus E: |x-y| < 2 \\operatorname{dist}(x,E)\\}$, $y \\in E$, defined on general closed subsets $E \\subset \\mathbb{R}^n$ supporting a non-homogeneous measure $\\mu$. We obtain boundedness criteria in this generality in terms of weak type testing of measures on regular balls $B \\subset E$, which are doubling and of small boundary. Due to the general set $E$ we use metric space"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.04309","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"}