{"paper":{"title":"Best constants for two families of higher order critical Sobolev embeddings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daniel Spector, Itai Shafrir","submitted_at":"2018-04-19T07:46:36Z","abstract_excerpt":"In this paper we obtain the best constants in some higher order Sobolev inequalities in the critical exponent. These inequalities can be separated into two types: those that embed into $L^\\infty(\\mathbb{R}^N)$ and those that embed into slightly larger target spaces. Concerning the former, we show that for $k \\in \\{1,\\ldots, N-1\\}$, $N-k$ even, one has an optimal constant $c_k>0$ such that \\[ \\|u\\|_{L^\\infty} \\leq c_k \\int |\\nabla^k (-\\Delta)^{(N-k)/2} u|\\] for all $u \\in C^\\infty_c(\\mathbb{R}^N)$ (the case $k=N$ was handled in a recent paper by Shafrir). Meanwhile the most significant of the l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07025","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"}