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

Author: T. S. Kopaliani

Source: Czechoslovak Mathematical Journal, Volume 54, Number 3, September 2004 , pp. 791-805(15)

Publisher: Springer

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

<IMG SRC="http://images.ingentaselect.com/absimages/klu/00114642/klu_cmaj_2004_54_3_426427h.1.gif" ALT="K f(x)=\varphi(x) \intˆx_0 k(x,y)f(y)\thinspace\psi (y) {\rm d}y" TEXT="a mathematical formula">

is studied, where k, , 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.

Keywords: Banach function space; uniformly upper; uniformly lower l-estimate; Hardy type operator

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10587-004-6427-3

Affiliations: 1: Department of Mechanics and Mathematics, Tbilisi State University, 1 Chavchavadze Ave., Tbilisi 380028, Georgia, Email: t_kopaliani@hotmail.com

Publication date: 2004-09-01

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