{"paper":{"title":"Weighted Bergman spaces induced by doubling weights in the unit ball of $\\mathbb{C}^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Juntao Du, Songxiao Li, Xiaosong Liu, Yecheng Shi","submitted_at":"2019-03-09T06:37:02Z","abstract_excerpt":"This paper is devoted to the study of the weighted Bergman space $A_\\omega^p $ in the unit ball $\\mathbb{B}$ of $\\mathbb{C}^n$ with doubling weight $\\omega$ satisfying $$\\int_r^1\\omega(t)dt <C \\int_{\\frac{1+r}{2}}^1\\omega(t)dt ,\\,\\, 0\\leq r<1.$$\n  The $q-$Carleson measures for $A_\\omega^p$ are characterized in terms of a neat geometric condition involving Carleson block. Some equivalent characterizations for $A_\\omega^p$ are obtained by using the radial derivative and admissible approach regions. The boundedness and compactness of Volterra integral operator $T_g:A_\\omega^p\\to A_\\omega^q$ are a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.03748","kind":"arxiv","version":2},"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"}