{"paper":{"title":"Sobolev Spaces of Fractional Order, Lipschitz Spaces, Readapted Modulation Spaces and Their Interrelations; Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Gerhard Schmeisser, Paul L. Butzer, Rudolf L. Stens","submitted_at":"2016-05-04T15:09:07Z","abstract_excerpt":"The purpose of this investigation is to extend basic equations and inequalities which hold for functions $f$ in a Bernstein space $B_\\sigma^2$ to larger spaces by adding a remainder term which involves the distance of $f$ from $B_\\sigma^2$.\n  First we present a modification of the classical modulation space $M^{2,1}(\\mathbb{R})$, the so-called readapted modulation space $M^{2,1}_\\text{a}(\\mathbb{R})$. Our approach to the latter space and its role in functional analysis is novel. In fact, we establish several chains of inclusion relations between $M^{2,1}_\\text{a}(\\mathbb{R})$ and the more comm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02777","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"}