{"paper":{"title":"Hardy spaces for semigroups with Gaussian bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Jacek Dziuba\\'nski, Marcin Preisner","submitted_at":"2016-06-03T12:40:47Z","abstract_excerpt":"Let T_t=e^{-tL} be a semigroup of self-adjoint linear operators acting on L^2(X,mu), where (X,d mu) is a space of homogeneous type. We assume that T_t has an integral kernel T_t(x,y) which satisfies the upper and lower Gaussian bounds: \\frac{C_1}{mu(B(x,\\sqrt{t}))} \\exp(-c_1d(x,y)^2/t)\\leq T_t(x,y) \\leq \\frac{C_2}{\\mu(B(x,\\sqrt{t}))} \\exp(-c_2 d(x,y)^2/t). By definition, f belongs to H^1_L if \\| f\\|_{H^1_L}=\\|\\sup_{t>0}|T_t f(x)|\\|_{L^1(X,\\mu)} <\\infty. We prove that there is a function \\omega(x), 0<c \\leq \\omega(x) \\leq C, such that H^1_L admits an atomic decomposition with atoms satisfying: "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01064","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"}