{"paper":{"title":"Characterization of the variable exponent Bessel potential spaces via the Poisson semigroup","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Humberto Rafeiro, Stefan Samko","submitted_at":"2009-04-22T22:43:13Z","abstract_excerpt":"Under the standard assumptions on the variable exponent $p(x)$ (log- and decay conditions), we give a characterization of the variable exponent Bessel potential space $\\mathfrak B^\\alpha[L^{p(\\cdot)}(\\mathbb R^n)]$ in terms of the rate of convergence of the Poisson semigroup $P_t$. We show that the existence of the Riesz fractional derivative $\\mathbb{D}^\\al f$ in the space $L^{p(\\cdot)}(\\rn)$ is equivalent to the existence of the limit $\\frac{1}{\\ve^\\al}(I-P_\\ve)^\\al f$. In the pre-limiting case $\\sup_x p(x)<\\frac{n}{\\al}$ we show that the Bessel potential space is characterized by the condit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.3567","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"}