On Compactness of Regular Integral Operators in the Space L1

Abstract

In this paper we obtain a sufficient condition for quite continuity of Fredholm type integral operators in the space L₁(a, b). Uniform approximations by operators with degenerate kernels of horizontally striped structures are constructed. A quantitative error estimate is obtained. We point out the possibility of application of the obtained results to second kind integral equations, including convolution equations on a finite interval, equations with polar kernels, one-dimensional equations with potential type kernels, and some transport equations in non-homogeneous layers.