Multilinear Generalizations of p-Summing, p-Integral, and p-Nuclear Operators

This paper establishes a comprehensive theory of operator ideals for multilinear mappings between Banach spaces, extending the classical linear theory developed by Pietsch [7] and the subsequent Lipschitz theory initiated by Farmer and Johnson [4].We introduce and characterize three fundamental classes of multilinear operators: strictly multilinear p-summing, strongly multilinear p-integral, and strongly multilinear p-nuclear operators.Our approach leverages the linearization technique, where multilinear maps are studied through their associated linear operators on projective tensor products.The main results prove sharp composition theorems that generalize classical results of Persson and Pietsch [6] and Tomczak-Jaegermann [9], demonstrating that under appropriate exponent relations, the composition of ideal multilinear operators preserves ideal properties with precise norm estimates.