{"paper":{"title":"Pointwise Characterizations of Besov and Triebel-Lizorkin Spaces and Quasiconformal Mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA"],"primary_cat":"math.CA","authors_text":"Dachun Yang, Pekka Koskela, Yuan Zhou","submitted_at":"2010-04-30T11:45:42Z","abstract_excerpt":"In this paper, the authors characterize, in terms of pointwise inequalities, the classical Besov spaces $\\dot B^s_{p,\\,q}$ and Triebel-Lizorkin spaces $\\dot F^s_{p,\\,q}$ for all $s\\in(0,\\,1)$ and $p,\\,q\\in(n/(n+s),\\,\\infty],$ both in ${\\mathbb R}^n$ and in the metric measure spaces enjoying the doubling and reverse doubling properties. Applying this characterization, the authors prove that quasiconformal mappings preserve $\\dot F^s_{n/s,\\,q}$ on $\\rn$ for all $s\\in(0,\\,1)$ and $q\\in(n/(n+s),\\,\\infty]$. A metric measure space version of the above morphism property is also established."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.5507","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"}