{"paper":{"title":"Fractional powers of the parabolic Hermite operator. Regularity properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jos\\'e L. Torrea, Marta de Le\\'on-Contreras","submitted_at":"2017-08-09T11:26:38Z","abstract_excerpt":"Let $\\mathcal{L}= \\partial_t- \\Delta_x+|x|^2$. Consider its Poisson semigroup $e^{-y\\sqrt{\\mathcal{L}}}$. For $\\alpha >0$ define the Parabolic Hermite-Zygmund spaces\n  $$\n  \\Lambda^\\alpha_{\\mathcal{L}}=\\left\\{f: \\:f\\in L^\\infty(\\mathbb{R}^{n+1})\\:\\; {\\rm and} \\:\\; \\left\\|\\partial_y^k e^{-y\\sqrt{\\mathcal{L}}} f \\right\\|_{L^\\infty(\\mathbb{R}^{n+1})}\\leq C_k y^{-k+\\alpha},\\;\\: {\\rm with }\\, k=[\\alpha]+1, y>0. \\right\\},\n  $$\n  with the obvious norm. It is shown that these spaces have a pointwise description of H\\\"older type.\n  The fractional powers $\\mathcal{L}^{\\pm \\beta}$ are well defined in the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02788","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"}