{"paper":{"title":"Density of smooth functions in variable exponent Sobolev spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Nikos Yannakakis, Thanasis Kostopoulos","submitted_at":"2014-06-20T13:45:20Z","abstract_excerpt":"We show that if $p_-\\geq 2$, then a sufficient condition for the density of smooth functions with compact support, in the variable exponent Sobolev space $W^{1,p(\\cdot)}(\\mathbb R^n)$, is that the Riesz potentials of compactly supported functions of $L^{p(\\cdot)}(\\mathbb R^n)$, are also elements of $L^{p(\\cdot)}(\\mathbb R^n)$. Using this result we then prove that the above density holds if (i) $p_-\\geq n$ or if (ii) $2\\leq p_-< n$ and $p_+<\\frac{np_-}{n-p_-}$. Moreover our result allows us to give an alternative proof, for the case $p_-\\geq 2$, that the local boundedness of the maximal operato"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5385","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"}