{"paper":{"title":"Interpolation for Hardy Spaces: Marcinkiewicz decomposition, Complex Interpolation and Holomorphic Martingales","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Paul F.X. M\\\"uller, Peter Yuditskii","submitted_at":"2016-09-23T13:52:28Z","abstract_excerpt":"The real and complex interpolation spaces for the classical Hardy spaces $H^1$ and $H^\\infty$ were determined in 1983 by P.W. Jones. Due to the analytic constraints the associated Marcinkiewicz decomposition gives rise to a delicate approximation problem for the $L^ 1$ metric. Specifically for $ f \\in H^p$ the size of $$ {\\rm{inf}} \\{ \\| f - f_1 \\| _1 \\,:\\, f_1 \\in H^\\infty ,\\, \\|f_1\\|_\\infty \\le \\lambda \\}$$ needs to be determined for any $ \\lambda>0 $. In the present paper we develop a new set of truncation formulae for obtaining the Marcinkiewicz decomposition of $(H^1, H^\\infty) $. We revi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07364","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"}