{"paper":{"title":"On weak$^*$-convergence in $H^1_L(\\mathbb R^d)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Luong Dang Ky","submitted_at":"2012-05-11T14:52:20Z","abstract_excerpt":"Let $L= -\\Delta+ V$ be a Schr\\\"odinger operator on $\\mathbb R^d$, $d\\geq 3$, where $V$ is a nonnegative function, $V\\ne 0$, and belongs to the reverse H\\\"older class $RH_{d/2}$. In this paper, we prove a version of the classical theorem of Jones and Journ\\'e on weak$^*$-convergence in the Hardy space $H^1_L(\\mathbb R^d)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2542","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"}