{"paper":{"title":"On weighted mixed-norm Sobolev estimates for some basic parabolic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA"],"primary_cat":"math.AP","authors_text":"J. L. Torrea, L. Ping, P. R. Stinga","submitted_at":"2016-02-02T00:43:44Z","abstract_excerpt":"Novel global weighted parabolic Sobolev estimates, weighted mixed-norm estimates and a.e. convergence results of singular integrals for evolution equations are obtained. Our results include the classical heat equation, the harmonic oscillator evolution equation $$\\partial_tu=\\Delta u-|x|^2u+f,$$ and their corresponding Cauchy problems. We also show weighted mixed-norm estimates for solutions to degenerate parabolic extension problems arising in connection with the fractional space-time nonlocal equations $(\\partial_t-\\Delta)^su=f$ and $(\\partial_t-\\Delta+|x|^2)^su=f$, for $0<s<1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00757","kind":"arxiv","version":4},"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"}