Ideals of multilinear mappings via Orlicz spaces and translation invariant operators
[EN] We study some new summability properties of multilinear operators. We introduce the concepts of phi-summing, phi semi-integral and phi-dominated multilinear maps generated by Orlicz functions. We prove a variant of Pietsch's domination theorem for phi-summing operators, providing also...
| Autores: | , |
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| Formato: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Recursos: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/189489 |
| Acesso em linha: | https://riunet.upv.es/handle/10251/189489 |
| Access Level: | acceso abierto |
| Palavra-chave: | Factorization theorems Haar measure Multilinear ideals Orlicz spaces Translation invariant operators MATEMATICA APLICADA |
| Resumo: | [EN] We study some new summability properties of multilinear operators. We introduce the concepts of phi-summing, phi semi-integral and phi-dominated multilinear maps generated by Orlicz functions. We prove a variant of Pietsch's domination theorem for phi-summing operators, providing also a characterization of phi-dominated operators in terms of factorizations. We analyze vector-valued inequalities associated to these maps, which are applied to obtain general variants of multiple summing operators. We also study translation invariant multilinear operators acting in products of spaces of continuous functions, proving that a factorization theorem can be obtained for them as a consequence of a suitable representation of the corresponding normalized Haar measure. |
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