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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1504.05636","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-04-22T02:35:34Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"3981879d84e8cc3fcce1ae7f38070414ab81a901adb09eede42a554d78d14750","abstract_canon_sha256":"d878c8a51cb0039fac202cb76ecd52fb8ab309e06c5c2506262605fa1ff724ed"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:13.098168Z","signature_b64":"7n6ikE1Hc03wkTqGbpVNrq29Mkjadora48qa22awuYIcCXwebwo7XfH+1vFtKe/FZlLCoShuf4Q95v610RcjBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8b0d89b6928b0b8b84617c6c73abcb8f541776eb194de9296094e598e6defd30","last_reissued_at":"2026-05-18T02:18:13.097551Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:13.097551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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]. 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