Strong Factorizations of Operators with Applications to Fourier and Cesàro Transforms
Consider two continuous linear operators T : X1(μ) ! Y1( ) and S : X2(μ) ! Y2( ) between Banach function spaces related to different -finite measures μ and . We characterize by means of weighted norm inequalities when T can be strongly factored through S, that is, when there exist functions g and h...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/103721 |
| Acceso en línea: | https://hdl.handle.net/11441/103721 https://doi.org/10.1307/mmj/1548817532 |
| Access Level: | acceso abierto |
| Palabra clave: | Banach function space Strong factorization Schauder basis Fourier operator Representing operator Cesáro operator |
| Sumario: | Consider two continuous linear operators T : X1(μ) ! Y1( ) and S : X2(μ) ! Y2( ) between Banach function spaces related to different -finite measures μ and . We characterize by means of weighted norm inequalities when T can be strongly factored through S, that is, when there exist functions g and h such that T (f) = gS(hf) for all f 2 X1(μ). For the case of spaces with Schauder basis our characterization can be improved, as we show when S is for instance the Fourier operator, or the Ces`aro operator. Our aim is to study the case when the map T is besides injective. Then we say that it is a representing operator —in the sense that it allows to represent each elements of the Banach function space X(μ) by a sequence of generalized Fourier coefficients—, providing a complete characterization of these maps in terms of weighted norm inequalities. Some examples and applications involving recent results on the Hausdorff-Young and the Hardy-Littlewood inequalities for operators on weighted Banach function spaces are also provided. |
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