{"paper":{"title":"Atomic decomposition of product Hardy spaces via wavelet bases on spaces of homogeneous type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ji Li, Lesley A. Ward, M. Cristina Pereyra, Yongsheng Han","submitted_at":"2018-10-09T03:10:17Z","abstract_excerpt":"We provide an atomic decomposition of the product Hardy spaces $H^p(\\widetilde{X})$ which were recently developed by Han, Li, and Ward in the setting of product spaces of homogeneous type $\\widetilde{X} = X_1 \\times X_2$. Here each factor $(X_i,d_i,\\mu_i)$, for $i = 1$, $2$, is a space of homogeneous type in the sense of Coifman and Weiss.\n  These Hardy spaces make use of the orthogonal wavelet bases of Auscher and Hyt\\\"onen and their underlying reference dyadic grids.\n  However, no additional assumptions on the quasi-metric or on the doubling measure for each factor space are made. To carry o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.03788","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"}