{"paper":{"title":"A Local Version of Hardy-type Spaces Associated with Ball Quasi-Banach Spaces and Non-negative Self-adjoint Operators on Spaces of Homogeneous Type and Their Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Tiantian Zhao, Wenhua Wang, Xiong Liu","submitted_at":"2025-03-05T09:34:39Z","abstract_excerpt":"Let $(\\mathbb{X},\\,d,\\,\\mu)$ be a space of homogeneous type in the sense of Coifman and Weiss, $X$ be a ball quasi-Banach function space on $\\mathbb{X}$, $L$ be a non-negative self-adjoint operator on $L^2(\\mathbb{X})$, and assume that, for all $t>0$, the semigroup $e^{-tL}$ has an integral representation whose kernel satisfies a Gaussian upper bound condition. In this paper, we first study a local version of Hardy space $h^{X}_L(\\mathbb{X})$ associated with ball quasi-Banach space $X$ and non-negative self-adjoint operator $L$, which is an extension of Goldberg's result [Duke Math. J. {\\bf46}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.03301","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.03301/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}