{"paper":{"title":"Herz-Type Hardy Spaces Associated with Ball Quasi-Banach Function Spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Aiting Wang, Baode Li, Mingquan Wei, Wenhua Wang","submitted_at":"2023-09-10T03:55:43Z","abstract_excerpt":"Let $X$ be a ball quasi-Banach function space, $\\alpha\\in \\mathbb{R}$ and $q\\in(0,\\infty)$. In this paper, the authors first introduce the Herz-type Hardy space $\\mathcal{H\\dot{K}}_{X}^{\\alpha,\\,q}({\\mathbb {R}}^n)$, which is defined via the non-tangential grand maximal function. Under some mild assumptions on $X$, the authors establish the atomic decompositions of $\\mathcal{H\\dot{K}}_{X}^{\\alpha,\\,q}({\\mathbb {R}}^n)$. As an application, the authors\n  obtain the boundedness of certain sublinear operators from $\\mathcal{H\\dot{K}}_{X}^{\\alpha,\\,q}({\\mathbb {R}}^n)$ to $\\mathcal{\\dot{K}}_{X}^{\\a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.12271","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2310.12271/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"}