On the Theory of Partial Integral Operators

The fundamental work of F. Riesz and J. Schauder has shown that the basic facts of the classical theory of integral equations (convergence of iteration methods, Fredholm alternative, bilinear expansions of kernels, etc.) are due to certain functional-analytic and geometric properties of corresponding integral transforms, such as boundedness (continuity), compactness, or weak compactness. With regard to this fact, many authors tried to find conditions for the continuity or compactness of linear integral operators in various function spaces. Now the theory of such operators is rather advanced and complete; the basic results may be found, for example, in the monographs

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