{"paper":{"title":"Frame decomposition and radial maximal semigroup characterization of Hardy spaces associated to operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ji Li, Liang Song, Lixin Yan, Xuan Thinh Duong","submitted_at":"2019-03-05T07:35:10Z","abstract_excerpt":"Let $L$ be the generator of an analytic semigroup whose kernels satisfy Gaussian upper bounds and H\\\"older's continuity. Also assume that $L$ has a bounded holomorphic functional calculus on $L^2(\\mathbb{R}^n)$. In this paper, we construct a frame decomposition for the functions belonging to the Hardy space $H_{L}^{1}(\\mathbb{R}^n)$ associated to $L$, and for functions in the Lebesgue spaces $L^p$, $1<p<\\infty$. We then show that the corresponding $H_{L}^{1}(\\mathbb{R}^n)$-norm (resp. $L^p(\\mathbb{R}^n)$-norm) of a function $f$ in terms of the frame coefficients is equivalent to the $H_{L}^{1}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.01705","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"}