{"paper":{"title":"A Generalization of Exponential Class and its Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chao Liu, Hong Tian, Hongya Gao","submitted_at":"2018-12-19T09:47:26Z","abstract_excerpt":"A function space, $L^{\\theta,\\infty)}(\\Omega)$, $0 \\leq \\theta <\\infty$, is defined. It is proved that $L^{\\theta,\\infty)}(\\Omega)$ is a Banach space which is a generalization of exponential class. An alternative definition of $L^{\\theta,\\infty)}(\\Omega)$ space is given. As an application, we obtain weak monotonicity property for very weak solutions of $\\mathcal{A}$-harmonic equation with variable coefficients under some suitable conditions related to $L^{\\theta,\\infty)}(\\Omega)$, which provides a generalization of a known result due to Moscariello. A weighted space $L^{\\theta,\\infty)}_w(\\Omeg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.07843","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"}