{"paper":{"title":"On integral equations related to weighted Toepitz operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Carme Cascante, Daniel Pascuas, Joan Fabrega","submitted_at":"2010-09-16T09:36:49Z","abstract_excerpt":"For weighted Toeplitz operators $\\T^N_\\phi$ defined on spaces of holomorphic functions in the unit ball, we derive regularity properties of the solutions $f$ to the integral equation $\\T^N_\\phi(f)=h$ in terms of the regularity of the symbol $\\phi$ and the data $h$. As an application, we deduce that if $f\\not\\equiv0$ is a function in the Hardy space $H^1$ such that its argument $\\bar f/f$ is in a Lipschitz space on the unit sphere $\\bB$, then $f$ is also in the same Lipschitz space, extending a result of K. Dyakonov to several complex variables."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3128","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"}