{"paper":{"title":"Anisotropic Singular Integrals in Product Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Baode Li, Dachun Yang, Marcin Bownik, Yuan Zhou","submitted_at":"2009-03-27T01:09:31Z","abstract_excerpt":"Let $A_i$ for $i=1, 2$ be an expansive dilation, respectively, on ${\\mathbb R}^n$ and ${\\mathbb R}^m$ and $\\vec A\\equiv(A_1, A_2)$. Denote by ${\\mathcal A}_\\infty(\\rnm; \\vec A)$ the class of Muckenhoupt weights associated with $\\vec A$. The authors introduce a class of anisotropic singular integrals on $\\mathbb R^n\\times\\mathbb R^m$, whose kernels are adapted to $\\vec A$ in the sense of Bownik and have vanishing moments defined via bump functions in the sense of Stein. Then the authors establish the boundedness of these anisotropic singular integrals on $L^q_w(\\mathbb R^n\\times\\mathbb R^m)$ wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.4720","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"}