{"paper":{"title":"Schauder estimates in generalized H\\\"older spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jongchun Bae, Moritz Kassmann","submitted_at":"2015-05-20T19:44:16Z","abstract_excerpt":"We prove Schauder estimates in generalized H\\\"older spaces $C^\\psi(\\mathbb{R}^d)$. These spaces are characterized by a general modulus of continuity $\\psi$, which cannot be represented by a real number. We consider linear operators $\\mathcal{L}$ between such spaces. The operators $\\mathcal{L}$ under consideration are integrodifferential operators with a functional order of differentiability $\\varphi$ which, again, is not represented by a real number. Assuming that $\\mathcal{L}$ has $\\psi$-continuous coefficients, we prove that solutions $u \\in C^{\\varphi\\psi}(\\mathbb{R}^d)$ to linear equations"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05498","kind":"arxiv","version":2},"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"}