{"paper":{"title":"Operator-valued local Hardy spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Runlian Xia, Xiao Xiong","submitted_at":"2018-03-27T20:58:38Z","abstract_excerpt":"This paper gives a systematic study of operator-valued local Hardy spaces. These spaces are localizations of the Hardy spaces defined by Tao Mei, and share many properties with Mei's Hardy spaces. We prove the ${\\rm h}_1$-$\\rm bmo$ duality, as well as the ${\\rm h}_p$-${\\rm h}_q$ duality for any conjugate pair $(p,q)$ when $1<p< \\infty$. We show that ${\\rm h}_1(\\mathbb{R}^d, \\mathcal M)$ and ${\\rm bmo}(\\mathbb{R}^d, \\mathcal M)$ are also good endpoints of $L_p(L_\\infty(\\mathbb{R}^d) \\overline{\\otimes} \\mathcal M)$ for interpolation. We obtain the local version of Calder\\'on-Zygmund theory, and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10321","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"}