{"paper":{"title":"Wavelet Coorbit Spaces viewed as Decomposition Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Felix Voigtlaender, Hartmut F\\\"uhr","submitted_at":"2014-04-16T16:09:14Z","abstract_excerpt":"In this paper we show that the Fourier transform induces an isomorphism between the coorbit spaces defined by Feichtinger and Gr\\\"ochenig of the mixed, weighted Lebesgue spaces $L_{v}^{p,q}$ with respect to the quasi-regular representation of a semi-direct product $\\mathbb{R}^{d}\\rtimes H$ with suitably chosen dilation group $H$, and certain decomposition spaces $\\mathcal{D}\\left(\\mathcal{Q},L^{p},\\ell_{u}^{q}\\right)$ (essentially as introduced by Feichtinger and Gr\\\"obner), where the localized ,,parts`` of a function are measured in the $\\mathcal{F}L^{p}$-norm.\n  This equivalence is useful in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4298","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"}