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On some structural properties of Banach function spaces and boundedness of certain integral operators

T. S. Kopaliani — 2004

Czechoslovak Mathematical Journal

In this paper the notions of uniformly upper and uniformly lower $ℓ$ -estimates for Banach function spaces are introduced. Further, the pair $(X, Y)$ of Banach function spaces is characterized, where $X$ and $Y$ satisfy uniformly a lower $ℓ$ -estimate and uniformly an upper $ℓ$ -estimate, respectively. The integral operator from $X$ into $Y$ of the form $K f (x) = ϕ (x) \int_{0}^{x} k (x, y) f (y) ψ (y) d y$ is studied, where $k$ , $ϕ$ , $ψ$ are prescribed functions under some local integrability conditions, the kernel $k$ is non-negative and is assumed to satisfy certain additional...

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