{"paper":{"title":"Paraexponentials, Muckenhoupt weights, and resolvents of paraproducts","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Cristina Pereyra, Lesley Ward","submitted_at":"1996-04-29T00:00:00Z","abstract_excerpt":"We analyze the stability of Muckenhoupt's $\\RHp$ and $\\Ap$ classes of weights under a nonlinear operation, the $\\lb$-operation. We prove that the dyadic doubling reverse H\\\"older classes $\\RHp$ are not preserved under the $\\lb$-operation, but the dyadic doubling $A_p$ classes $\\Ap$ are preserved for $0<\\lb <1$. We give an application to the structure of resolvent sets of dyadic paraproduct operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9604229","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"}