{"paper":{"title":"Absolutely summing operators and atomic decomposition in bi-parameter Hardy spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Johanna Penteker, Paul F.X. M\\\"uller","submitted_at":"2015-12-15T14:07:18Z","abstract_excerpt":"For $f \\in H^p(\\delta^2)$, $0<p\\leq 2$, with Haar expansion $f=\\sum f_{I \\times J}h_{I\\times J}$ we constructively determine the Pietsch measure of the $2$-summing multiplication operator\n  \\[\\mathcal{M}_f:\\ell^{\\infty} \\rightarrow H^p(\\delta^2), \\quad (\\varphi_{I\\times J}) \\mapsto \\sum \\varphi_{I\\times J}f_{I \\times J}h_{I \\times J}. \\] Our method yields a constructive proof of Pisier's decomposition of $f \\in H^p(\\delta^2)$\n  \\[|f|=|x|^{1-\\theta}|y|^{\\theta}\\quad\\quad \\text{ and }\\quad\\quad \\|x\\|_{X_0}^{1-\\theta}\\|y\\|^{\\theta}_{H^2(\\delta^2)}\\leq C\\|f\\|_{H^p(\\delta^2)}, \\] where $X_0$ is Pis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04790","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":""},"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"}