{"paper":{"title":"Equivalence of Littlewood-Paley square function and area function characterizations of weighted product Hardy spaces associated to operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Guorong Hu, Ji Li, Xuan Thinh Duong","submitted_at":"2017-06-19T06:55:20Z","abstract_excerpt":"Let $L_{1}$ and $L_{2}$ be non-negative self-adjoint operators acting on $L^{2}(X_{1})$ and $L^{2}(X_{2})$, respectively, where $X_{1}$ and $X_{2}$ are spaces of homogeneous type. Assume that $L_{1}$ and $L_{2}$ have Gaussian heat kernel bounds. This paper aims to study some equivalent characterizations of the weighted product Hardy spaces $H^{p}_{w,L_{1},L_{2}}(X_{1}\\times X_{2})$ associated to $L_{1}$ and $L_{2}$, for $p \\in (0, \\infty)$ and the weight $w$ belongs to the product Muckenhoupt class $A_{\\infty}(X_{1} \\times X_{2})$. Our main result is that the spaces $H^{p}_{w,L_{1},L_{2}}(X_{1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05803","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"}