{"paper":{"title":"p-Summing Multiplication Operators, dyadic Hardy Spaces and atomic Decomposition","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":"2013-10-16T09:56:28Z","abstract_excerpt":"We constructively determine the Pietsch measure of the 2-summing multiplication operator\n  \\[\\mathcal{M}_u:\\ell^{\\infty} \\rightarrow H^p, \\quad (\\varphi_I) \\mapsto \\sum \\varphi_Ix_Ih_I. \\] Our construction of the Pietsch measure for the multiplication operator $\\mathcal{M}_u$ involves the Haar coefficients of $u$ and its atomic decomposition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4312","kind":"arxiv","version":4},"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"}