{"paper":{"title":"Equivalence of sparse and Carleson coefficients for general sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Timo S. Hanninen","submitted_at":"2017-09-29T15:35:22Z","abstract_excerpt":"We remark that sparse and Carleson coefficients are equivalent for every countable collection of Borel sets and hence, in particular, for dyadic rectangles, the case relevant to the theory of bi-parameter singular integrals.\n  The key observation is that a dual refomulation by I. E. Verbitsky for Carleson coefficients over dyadic cubes holds also for Carleson coefficients over general sets. We give a simple proof for this reformulation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.10457","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"}