{"paper":{"title":"End-point estimates for singular integrals with non-smooth kernels on product spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ji Li, Lixin Yan, Xuan Thinh Duong","submitted_at":"2015-09-24T22:02:49Z","abstract_excerpt":"The main aim of this article is to establish boundedness of singular integrals with non-smooth kernels on product spaces. Let $L_1$ and $L_2$ be non-negative self-adjoint operators on $L^2(\\mathbb{R}^{n_1})$ and $L^2(\\mathbb{R}^{n_2})$, respectively, whose heat kernels satisfy Gaussian upper bounds. First, we obtain an atomic decomposition for functions in $H^1_{L_1,L_2}(\\mathbb{R}^{n_1}\\times\\mathbb{R}^{n_2})$ where the Hardy space $H^1_{L_1,L_2}(\\mathbb{R}^{n_1}\\times\\mathbb{R}^{n_2})$ associated with $L_1$ and $L_2$ is defined by square function norms, then prove an interpolation property f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07548","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"}