{"paper":{"title":"On dyadic nonlocal Schr\\\"{o}dinger equations with Besov initial data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bruno Bongioanni, Hugo Aimar, Ivana G\\'omez","submitted_at":"2012-06-05T13:33:19Z","abstract_excerpt":"In this paper we consider the pointwise convergence to the initial data for the Schr\\\"{o}dinger-Dirac equation $i\\tfrac{\\partial u}{\\partial t}=D^{\\beta}u$ with $u(x,0)=u^0$ in a dyadic Besov space. Here $D^{\\beta}$ denotes the fractional derivative of order $\\beta$ associated to the dyadic distance $\\delta$ on $\\mathbb{R}^+$. The main tools are a sumability formula for the kernel of $D^{\\beta}$ and pointwise estimates of the corresponding maximal operator in terms of the dyadic Hardy-Littlewood function and the Calder\\'on sharp maximal operator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0926","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"}