Maximal weak Orlicz types and the strong maximal operator on von Neumann algebras
Let En: M → Mn and Em: N → Nm be two sequences of conditional expectations on finite von Neumann algebras. The optimal weak Orlicz type of the associated strong maximal operator E = (En ⊗ Em)n,m is not yet known. In a recent work of Jose Conde and the first two authors, it was shown that E has weak...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repositorio: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:digital.csic.es:10261/423091 |
| Acceso en línea: | http://hdl.handle.net/10261/423091 https://www.scopus.com/inward/record.uri?eid=2-s2.0-105024438203&doi=10.4064%2Fsm240522-15-7&partnerID=40&md5=2bc4d7e040065f3a6e1d238ecb243f7e |
| Access Level: | acceso abierto |
| Palabra clave: | maximal operators noncommutative analysis Orlicz spaces |
| Sumario: | Let En: M → Mn and Em: N → Nm be two sequences of conditional expectations on finite von Neumann algebras. The optimal weak Orlicz type of the associated strong maximal operator E = (En ⊗ Em)n,m is not yet known. In a recent work of Jose Conde and the first two authors, it was shown that E has weak type (Φ, Φ) for a family of functions including Φ(t) = t log2+ε t for every ε > 0. We prove that the weak Orlicz type of E cannot be lowered below L log2 L, meaning that if E is of weak type (Φ, Φ), then Φ(s) ∉ o(s log2 s). Our proof is based on interpolation. We use recent techniques of Cadilhac/Ricard to formulate a Marcinkiewicz-type theorem for maximal weak Orlicz types. Then, we show that a weak Orlicz type lower than L log2 L would imply a p-operator constant for E smaller than the known optimum as p → 1+. © Instytut Matematyczny PAN, 2025. |
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