{"paper":{"title":"Cauchy-type integrals in several complex variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Elias M. Stein, Loredana Lanzani","submitted_at":"2013-11-20T19:05:29Z","abstract_excerpt":"We present the theory of Cauchy-Fantappi\\'e integral operators, with emphasis on the situation when the domain of integration, $D$, has minimal boundary regularity. Among these operators we focus on those that are more closely related to the classical Cauchy integral for a planar domain, whose kernel is a holomorphic function of the parameter $z\\in D$. The goal is to prove $L^p$ estimates for these operators and, as a consequence, to obtain $L^p$ estimates for the canonical Cauchy-Szeg\\\"o and Bergman projection operators (which are not of Cauchy-Fantappi\\'e type)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.5175","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"}