{"paper":{"title":"Weak Hardy Spaces $WH_L^p({\\mathbb R}^n)$ Associated to Operators Satisfying $k$-Davies-Gaffney Estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Dachun Yang, Der-Chen Chang, Huoxiong Wu, Jun Cao","submitted_at":"2013-08-25T08:01:48Z","abstract_excerpt":"Let $L$ be a one-to-one operator of type $\\omega$ having a bounded $H_\\infty$ functional calculus and satisfying the $k$-Davies-Gaffney estimates with $k\\in{\\mathbb N}$. In this paper, the authors introduce the weak Hardy space $WH_L^p(\\mathbb{R}^n)$ associated to $L$ for $p\\in (0,\\,1]$ via the non-tangential square function $S_L$ and establish a weak molecular characterization of $WH_L^p(\\mathbb{R}^n)$. Typical examples of such operators include the $2k$-order divergence form homogeneous elliptic operator $L_1:=(-1)^k\\sum_{|\\alpha|=k=|\\beta|}\\partial^\\beta(a_{\\alpha,\\beta}\\partial^\\alpha)$, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5385","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"}