{"paper":{"title":"Preduals of quadratic Campanato spaces associated to operators with heat kernel bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jie Xiao, Liang Song, Xuefang Yan","submitted_at":"2014-02-24T04:12:05Z","abstract_excerpt":"Let $L$ be a nonnegative, self-adjoint operator on $L^2(\\mathbb{R}^n)$ with the Gaussian upper bound on its heat kernel. As a generalization of the square Campanato space $\\mathcal{L}^{2,\\lambda}_{-\\Delta}(\\mathbb R^n)$, in \\cite{DXY} the quadratic Campanato space $\\mathcal{L}_L^{2,\\lambda}(\\mathbb{R}^n)$ is defined by a variant of the maximal function associated with the semigroup $\\{e^{-tL}\\}_{t\\geq 0}$. On the basis of \\cite{DX} and \\cite{YY} this paper addresses the preduality of $\\mathcal{L}_L^{2,\\lambda}(\\mathbb{R}^n)$ through an induced atom (or molecular) decomposition. Even in the cas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5717","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"}