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

Author： Kopaliani T. S.  

Publisher： Springer Publishing Company

ISSN： 0011-4642

Source： Czechoslovak Mathematical Journal, Vol.54, Iss.3, 2004-09, pp. : 791-805

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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[ Equation s10587-004-6427-3_eq1.gif]is studied, where k, &phis;, 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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