LIPSCHITZ (q, p)-MIXING OPERATORS.

Several useful results in the theory of p-summing operators, such as Pietsch's composition theorem and Grothendieck's theorem, share a common form: for certain values q and p, there is an operator such that whenever it is followed by a q-summing operator, the composition is p-summing. This is precisely the concept of (q, p)-mixing operators, defined and studied by A. Pietsch. On the other hand, J. Farmer and W. B. Johnson recently introduced the notion of a Lipschitz p-summing operator, a nonlinear generalization of p-summing operators. In this paper, a corresponding nonlinear concept of Lipschitz (q, p)-mixing operators is introduced, and several characterizations of it are proved. An interpolation-style theorem relating different Lipschitz (q, p)-mixing constants is obtained, and it is used to show reversed inequalities between Lipschitz p-summing norms. [ABSTRACT FROM AUTHOR]