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On Some Structural Properties of Banach Function Spaces and Boundedness of Certain Integral Operators

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Abstract

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

$$Kf(x) = \varphi (x)\int\limits_0^x {k{\text{(}}x,y{\text{)}}f(y)\psi (y)dy} $$

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 conditions, notably one of monotone type.

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Authors and Affiliations

  1. Department of Mechanics and Mathematics, Tbilisi State University, 1 Chavchavadze Ave., Tbilisi, 380028, Georgia

    T. S. Kopaliani

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  1. T. S. Kopaliani
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Kopaliani, T.S. On Some Structural Properties of Banach Function Spaces and Boundedness of Certain Integral Operators. Czechoslovak Mathematical Journal 54, 791–805 (2004). https://doi.org/10.1007/s10587-004-6427-3

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  • DOI: https://doi.org/10.1007/s10587-004-6427-3

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