{"paper":{"title":"Tangential limits for harmonic functions with respect to $\\phi(\\Delta)$ : stable and beyond","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jaehoon Kang, Panki Kim","submitted_at":"2014-05-09T05:01:16Z","abstract_excerpt":"In this paper, we discuss tangential limits for regular harmonic functions with respect to $\\phi(\\Delta):=-\\phi(-\\Delta)$ in the $C^{1,1}$ open set $D$ in $\\mathbb{R}^d$, where $\\phi$ is the complete Bernstein function and $d \\ge 2$. When the exterior function $f$ is local $L^p$-H\\\"older continuous of order $\\beta$ on $D^c$ with $ p\\in(1,\\infty]$ and $\\beta>1/p$, for a large class of Bernstein function $\\phi$, we show that the regular harmonic function $u_f$ with respect to $\\phi(\\Delta)$, whose value is $f$ on $D^c$, converges a.e. through a certain parabola that depends on $\\phi$ and $\\phi'$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2141","kind":"arxiv","version":3},"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"}