{"paper":{"title":"The Fourier Transform of Anisotropic Hardy Spaces with Variable Exponents and Their Applications","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Aiting Wang, Wenhua Wang","submitted_at":"2021-12-21T03:10:48Z","abstract_excerpt":"Let $A$ be an expansive dilation on $\\mathbb{R}^n$, and $p(\\cdot):\\mathbb{R}^n\\rightarrow(0,\\,\\infty)$ be a variable exponent function satisfying the globally log-H\\\"{o}lder continuous condition. Let $\\mathcal{H}^{p(\\cdot)}_A({\\mathbb {R}}^n)$ be the variable anisotropic Hardy space defined via the non-tangential grand maximal function. In this paper, the authors obtain that the Fourier transform of $f\\in \\mathcal{H}^{p(\\cdot)}_A({\\mathbb {R}}^n)$ coincides with a continuous function $F$ on $\\mathbb{R}^n$ in the sense of tempered distributions. As applications, the authors further conclude a h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.10956","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/2112.10956/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"}