{"paper":{"title":"The Jones Strong Distribution Banach Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.FA","authors_text":"Tepper L. Gill","submitted_at":"2015-04-10T21:09:57Z","abstract_excerpt":"In this note, we introduce a new class of separable Banach spaces, ${SD^p}[{\\mathbb{R}^n}],\\;1 \\leqslant p \\leqslant \\infty$, which contain each $L^p$-space as a dense continuous and compact embedding. They also contain the nonabsolutely integrable functions and the space of test functions ${\\mathcal{D}}[{\\mathbb{R}^n}]$, as dense continuous embeddings. These spaces have the remarkable property that, for any multi-index $\\alpha, \\; \\left\\| {{D^\\alpha }{\\mathbf{u}}} \\right\\|_{SD} = \\left\\| {\\mathbf{u}} \\right\\|_{SD}$, where $D$ is the distributional derivative. We call them Jones strong distrib"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02794","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"}