{"paper":{"title":"Strichartz and smoothing estimates in weighted $L^2$ spaces and their applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ihyeok Seo, Youngwoo Koh","submitted_at":"2018-03-28T07:14:55Z","abstract_excerpt":"The primary objective in this paper is to give an answer to an open question posed by J. A. Barcel\\'o, J. M. Bennett, A. Carbery, A. Ruiz and M. C. Vilela concerning the problem of determining the optimal range on $s\\geq0$ and $p\\geq1$ for which the following Strichartz estimate with time-dependent weights $w$ in Morrey-Campanato type classes $\\mathfrak{L}^{2s+2,p}_2$ holds: \\begin{equation}\\label{absset} \\|e^{it\\Delta}f\\|_{L_{x,t}^2(w(x,t))}\\leq C\\|w\\|_{\\mathfrak{L}^{2s+2,p}_2}^{1/2}\\|f\\|_{\\dot{H}^s}. \\end{equation} Beyond the case $s\\geq0$, we further ask how much regularity we can expect on"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10430","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"}