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- W2592458049 abstract "Consider two continuous linear operators $Tcolon X_1(mu)to Y_1(nu)$ and $Scolon X_2(mu)to Y_2(nu)$ between Banach function spaces related to different $sigma$-finite measures $mu$ and $nu$. 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 $fin X_1(mu)$. For the case of spaces with Schauder basis our characterization can be improved, as we show when $S$ is for instance the Fourier 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 $X(mu)$ 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." @default.
- W2592458049 created "2017-03-16" @default.
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- W2592458049 date "2017-03-07" @default.
- W2592458049 modified "2023-10-13" @default.
- W2592458049 title "Strong factorizations of operators with applications to Fourier and Ces'aro transforms" @default.
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- W2592458049 doi "https://doi.org/10.48550/arxiv.1703.02260" @default.
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