{"paper":{"title":"Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Carlos Cabrelli, Jos\\'e Luis Romero, Ursula Molter","submitted_at":"2011-08-13T02:03:36Z","abstract_excerpt":"In this article we construct affine systems that provide a simultaneous atomic decomposition for a wide class of functional spaces including the Lebesgue spaces $L^p(\\Rdst)$, $1<p<+\\infty$. The novelty and difficulty of this construction is that we allow for non-lattice translations.\n  We prove that for an arbitrary expansive matrix $A$ and any set $\\Lambda$ - satisfying a certain spreadness condition but otherwise irregular- there exists a smooth window whose translations along the elements of $\\Lambda$ and dilations by powers of $A$ provide an atomic decomposition for the whole range of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2748","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"}