{"paper":{"title":"Essential Norms of Weighted Composition Operators between Hardy Spaces in the unit Ball","license":"","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Ze-Hua Zhou, Zhong-Shan Fang","submitted_at":"2007-09-10T16:13:00Z","abstract_excerpt":"Let $\\phi(z)=(\\phi_1(z),...,\\phi_n(z))$ be a holomorphic self-map of $B_n$ and $\\psi(z)$ a holomorphic function on $B_n$, and $H(B_n)$ the class of all holomorphic functions on $B_n$, where $B_n$ is the unit ball of $C^n$, the weight composition operator $W_{\\psi,\\phi}$ is defined by $W_{\\psi,\\phi}=\\psi f(\\phi)$ for $f\\in H(B_n)$. In this paper we estimate the essential norm for the weighted composition operator $W_{\\psi,\\phi}$ acting from the Hardy space $H^p$ to $H^q$ ($0<p,q\\leq \\infty$). When $p=\\infty$ and $q=2$, we give an exact formula for the essential norm. As their applications, we a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.1431","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"}