The Michigan Mathematical Journal
- Michigan Math. J.
- Volume 68, Issue 1 (2019), 167-192.
Strong Factorizations of Operators with Applications to Fourier and Cesàro Transforms
Consider two continuous linear operators and between Banach function spaces related to different -finite measures and . By means of weighted norm inequalities we characterize when can be strongly factored through , that is, when there exist functions and such that for all . For the case of spaces with Schauder basis, our characterization can be improved, as we show when is, for instance, the Fourier or Cesàro operator. Our aim is to study the case where the map 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 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.
Michigan Math. J., Volume 68, Issue 1 (2019), 167-192.
Received: 27 March 2017
Revised: 14 September 2018
First available in Project Euclid: 30 January 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Primary: 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 47B38: Operators on function spaces (general)
Secondary: 46B15: Summability and bases [See also 46A35] 43A25: Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups
Delgado, O.; Mastyło, M.; Sánchez Pérez, E. A. Strong Factorizations of Operators with Applications to Fourier and Cesàro Transforms. Michigan Math. J. 68 (2019), no. 1, 167--192. doi:10.1307/mmj/1548817532. https://projecteuclid.org/euclid.mmj/1548817532