Strong Factorizations of Operators with Applications to Fourier and Cesaro Transforms
[EN] Consider two continuous linear operators T: X-1 (mu) -> Y-1 (nu) and S: X-2 (mu) -> Y-2 (nu) between Banach function spaces related to different sigma-finite measures mu and nu. By means of weighted norm inequalities we characterize when T can be strongly factored through S, that...
| Authors: | , , |
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| Format: | article |
| Publication Date: | 2019 |
| Country: | España |
| Institution: | Universitat Politècnica de València (UPV) |
| Repository: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Language: | English |
| OAI Identifier: | oai:riunet.upv.es:10251/156255 |
| Online Access: | https://riunet.upv.es/handle/10251/156255 |
| Access Level: | Open access |
| Keyword: | Factorization Operator Fourier Transform Cesaro Transform MATEMATICA APLICADA |
| Summary: | [EN] Consider two continuous linear operators T: X-1 (mu) -> Y-1 (nu) and S: X-2 (mu) -> Y-2 (nu) between Banach function spaces related to different sigma-finite measures mu and nu. By means of weighted norm inequalities we characterize 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 is an element of X-1 (mu). For the case of spaces with Schauder basis, our characterization can be improved, as we show when S is, for instance, the Fourier or Cesar operator. Our aim is to study the case where the map T is besides injective. Then we say that it is a representing operator-in the sense that it allows us to represent each element of the Banach function space X (mu) by a sequence of generalized Fourier coefficients-providing a complete characterization of these maps in terms of weighted norm inequalities. We also provide some examples and applications involving recent results on the Hausdorff-Young and the Hardy-Littlewood inequalities for operators on weighted Banach function spaces. |
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