{"paper":{"title":"Improvement of a Hardy-Littlewood inequality and applications to the boundedness of analytic paraproducts on mixed norm spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA"],"primary_cat":"math.CV","authors_text":"\\'Alvaro Miguel Moreno, Jos\\'e \\'Angel Pel\\'aez","submitted_at":"2026-05-27T07:34:03Z","abstract_excerpt":"Let $\\mathcal{H}(\\mathbb{D})$ denote the space of analytic functions in the unit disc $\\mathbb{D}=\\{z\\in\\mathbb{C}:|z|<1\\}$. For $0<p<\\infty$ and $f\\in\\mathcal{H}(\\mathbb{D})$, let $M_p^p(r,f)=\\int_0^{2\\pi}|f(re^{i\\theta})|^p \\frac{d\\theta}{2\\pi}$ and $M_\\infty(r,f) = \\sup_{|z|=r}|f(z)|$.\n  For $0<p<q\\leq \\infty$, Hardy and Littlewood proved the prevalent inequality $$M_q(r,f)\\le C(p,q)\\frac{M_p(\\rho,f)}{(\\rho-r)^{\\frac{1}{p}-\\frac{1}{q}}}$$ for $0\\leq r<\\rho\\leq 1$ and $f\\in\\mathcal{H}(\\mathbb{D})$.\n  In this paper, we obtain an improvement of this well-known inequality which is employed to c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.28080","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/2605.28080/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"}