{"paper":{"title":"Weighted Besov and Triebel--Lizorkin spaces associated to operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Huy-Qui Bui, The Anh Bui, Xuan Thinh Duong","submitted_at":"2018-09-08T12:43:34Z","abstract_excerpt":"Let $X$ be a space of homogeneous type and $L$ be a nonnegative self-adjoint operator on $L^2(X)$ satisfying Gaussian upper bounds on its heat kernels. In this paper we develop the theory of weighted Besov spaces $\\dot{B}^{\\alpha,L}_{p,q,w}(X)$ and weighted Triebel--Lizorkin spaces $\\dot{F}^{\\alpha,L}_{p,q,w}(X)$ associated to the operator $L$ for the full range $0<p,q\\le \\infty$, $\\alpha\\in \\mathbb R$ and $w$ being in the Muckenhoupt weight class $A_\\infty$. Similarly to the classical case in the Euclidean setting, we prove that our new spaces satisfy important features such as continuous cha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02795","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"}