A GENERAL THEOREM
ON CONTINUITY AND COMPACTNESS
OF THE URYSON OPERATOR

MARTIN VÄTH

Abstract:

We consider the Uryson operator in a very general class of spaces, which in particular contains ideal spaces (e.g., -spaces and Orlicz spaces). We will prove a theorem which will allow us to construct growth conditions on the generating function, which assure that the operator is continuous and compact. The theorem is applied also for linear integral operators and for nonlinear Volterra-Uryson equations.