{"paper":{"title":"Riesz Transform Characterizations of Hardy Spaces Associated to Degenerate Elliptic Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Dachun Yang, Junqiang Zhang","submitted_at":"2015-09-18T00:26:09Z","abstract_excerpt":"Let $w$ be a Muckenhoupt $A_2(\\mathbb{R}^n)$ weight and $L_w:=-w^{-1}\\mathop\\mathrm{div}(A\\nabla)$ the degenerate elliptic operator on the Euclidean space $\\mathbb{R}^n$. In this article, the authors establish the Riesz transform characterization of the Hardy space $H_{L_w}^p(\\mathbb{R}^n)$ associated with $L_w$, for $w\\in A_{q}(\\mathbb{R}^n)$ and $w^{-1}\\in A_{2-\\frac{2}{n}}(\\mathbb{R}^n)$ with $n\\geq 3$, $q\\in[1,2]$ and $p\\in(q(\\frac{1}{r}+\\frac{q-1}{2}+\\frac{1}{n})^{-1},1]$ if, for some $r\\in[1,\\,2)$, $\\{tL_w e^{-tL_w}\\}_{t\\geq 0}$ satisfies the weighted $L^r-L^2$ full off-diagonal estimate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05479","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"}