{"paper":{"title":"Independence of derivatives in Carleman-Sobolev Classes for exponents $0<p<1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Aron Wennman","submitted_at":"2014-05-12T14:41:51Z","abstract_excerpt":"We continue the study of Carleman-Sobolev classes from previous joint work with G. Behm. We consider spaces denoted by $W_\\mathcal{M}^p$, defined as abstract completions of sets of smooth functions with respect to a weighted Sobolev-flavoured norm involving derivatives of all orders. Previously we showed that these classes behaves very differently on two sides of a condition on the weight sequence $\\mathcal{M}$. Here we prove a conjecture made in that paper; under some regularity assumptions on the weight, we show that on one side of the condition there will be a complete independence between "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2787","kind":"arxiv","version":3},"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"}