{"paper":{"title":"Vertical square functions and other operators associated with an elliptic operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Cruz Prisuelos-Arribas","submitted_at":"2018-05-13T10:09:19Z","abstract_excerpt":"We study the vertical and conical square functions defined via elliptic operators in divergence form. In general, vertical and conical square functions are equivalent operators just in $L^2$. But when this square functions are defined through the heat or Poisson semigroup that arise from an elliptic operator, we are able to find open intervals containing $2$ where the equivalence holds. The intervals in question depend ultimately on the range where the semigroup is uniformly bounded or has off-diagonal estimates. As a consequence we obtain new boundedness results for some square functions. Bes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04853","kind":"arxiv","version":3},"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"}