Article
Strong Factorizations of Operators with Applications to Fourier and Cesàro Transforms
Author/s | Delgado Garrido, Olvido
Mastylo, Mieczyslaw Sánchez Pérez, E. A. |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Publication Date | 2019 |
Deposit Date | 2021-01-14 |
Published in |
|
Abstract | 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 ... 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. |
Funding agencies | Ministerio de Economía y Competitividad (MINECO). España Junta de Andalucía |
Project ID. | MTM2015-65888-C4-1-P
FQM-7276 |
Citation | Delgado Garrido, O., Mastylo, M. y Sánchez Pérez, E.A. (2019). Strong Factorizations of Operators with Applications to Fourier and Cesàro Transforms. Michigan Mathematical Journal, 68 (1), 167-192. |
Files | Size | Format | View | Description |
---|---|---|---|---|
Strong Factorizations of Opera ... | 296.1Kb | [PDF] | View/ | |