{"paper":{"title":"$L^p-L^q$ estimates for the solution of the Dunkl wave equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"B\\'echir Amri, Mohamed Gaidi","submitted_at":"2017-06-27T17:31:07Z","abstract_excerpt":"In this paper, our main aim is to derive $L^p-L^q$ estimates of the solution $u_k(x,t)$ ( t fixed) of the Cauchy problem for the homogeneous linear wave equation associated to the Dunkl Laplacian $\\Delta_k$, $$\\Delta_ku_k(x,t)= \\partial_t^2u_k (x,t),\\quad \\partial_tu_k(x,0)= f(x),\\quad u_k(x,0)= g(x).$$ We extend to Dunkl setting the estimates given by Srichartz in \\cite{Sti} for the ordinary wave equation ."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08952","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"}