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Some new function spaces and their tensor products

The theory of the mapping properties of an integral operator K : A ->• B , where K is a fixed operator and the spaces A, B are to be found, has come to be called the theory of admissibility. In particular the behaviour of solutions to integral equations can be simply described within the framework of admissibility theory. In this theory a central role is played by Banach function spaces as defined in [4]; the wider the variety of Banach function spaces with which we are equipped, the more precisely can we specify the asymptotic or local properties of the solutions to an integral equation.