{"paper":{"title":"A priori H\\\"older and Lipschitz regularity for generalized $p$-harmonious functions in metric measure spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.AP","authors_text":"\\'Angel Arroyo, Jos\\'e G. Llorente","submitted_at":"2017-02-23T11:11:14Z","abstract_excerpt":"Let $(\\mathbb{X} , d, \\mu )$ be a proper metric measure space and let $\\Omega \\subset \\mathbb{X}$ be a bounded domain. For each $x\\in \\Omega$, we choose a radius $0< \\varrho (x) \\leq \\mathrm{dist}(x, \\partial \\Omega ) $ and let $B_x$ be the closed ball centered at $x$ with radius $\\varrho (x)$. If $\\alpha \\in \\mathbb{R}$, consider the following operator in $C( \\overline{\\Omega} )$, $$\n  \\mathcal{T}_{\\alpha}u(x)=\\frac{\\alpha}{2}\\left(\\sup_{B_x } u+\\inf_{B_x } u\\right)+(1-\\alpha)\\,\\frac{1}{\\mu(B_x)}\\int_{B_x}\\hspace{-0.1cm} u\\ d\\mu. $$ Under appropriate assumptions on $\\alpha$, $\\mathbb{X}$, $\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.07175","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"}