{"paper":{"title":"Maximal Function Characterizations of Hardy Spaces Associated to Homogeneous Higher Order Elliptic Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Dachun Yang, Jun Cao, Svitlana Mayboroda","submitted_at":"2015-04-22T02:35:34Z","abstract_excerpt":"Let $L$ be a homogeneous divergence form higher order elliptic operator with complex bounded measurable coefficients and $(p_-(L),\\, p_+(L))$ be the maximal interval of exponents $q\\in[1,\\,\\infty]$ such that the semigroup $\\{e^{-tL}\\}_{t>0}$ is bounded on $L^q(\\mathbb{R}^n)$. In this article, the authors establish the non-tangential maximal function characterizations of the associated Hardy spaces $H_L^p(\\mathbb{R}^n)$ for all $p\\in(0,\\,p_+(L))$, which, when $p=1$, answers a question asked by Deng et al. in [J. Funct. Anal. 263 (2012), 604-674]. Moreover, the authors characterize $H_L^p(\\mathb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05636","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"}