{"paper":{"title":"Discrete Hardy spaces and heat semigroup associated with the discrete Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Jorge J. Betancor, Lourdes Rodr\\'iguez Mesa, V\\'ictor Almeida","submitted_at":"2018-10-24T14:21:25Z","abstract_excerpt":"In this paper we study the behavior of some harmonic analysis operators associated with the discrete Laplacian $\\Delta_d$ in discrete Hardy spaces $\\mathcal H^p(\\mathbb Z)$. We prove that the maximal operator and the Littlewood-Paley $g$ function defined by the semigroup generated by $\\Delta_d$ are bounded from $\\mathcal H^p(\\mathbb Z)$ into $\\ell^p(\\mathbb Z)$, $0<p\\leq 1$. Also, we establish that every $\\Delta_d$-spectral multiplier of Laplace transform type is a bounded operator from $\\mathcal H^p(\\mathbb Z)$ into itself, for every $0<p\\leq 1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.10415","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"}