{"paper":{"title":"On harmonic quasiregular mappings in Bergman spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Antti Rasila, Suman Das","submitted_at":"2025-07-25T11:03:03Z","abstract_excerpt":"A classical result of Hardy and Littlewood says that if $f=u+iv$ is analytic in the unit disk $\\mathbb{D}$ and $u$ is in the harmonic Bergman space $a^p$ ($0<p<\\infty$), then $v$ is also in $a^p$. This complements a celebrated result of M. Riesz on Hardy spaces, which only holds for $1<p<\\infty$. These results do not extend directly to complex-valued harmonic functions. We prove that the Hardy-Littlewood theorem holds for a harmonic function $f=u+iv$ if we place the assumption that $f$ is quasiregular in $\\mathbb{D}$. This makes further progress on the recent Riesz type theorems for harmonic q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.19158","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/2507.19158/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"}