A Banach algebra of functions of several variables of finite total variation and Lipschitzian superposition operators. II

Abstract

We characterize superposition Nemytskii operators, which map the Banach algebra of functions of n real variables with finite total variation in the sense of Vitali, Hardy and Krause into itself and satisfy the global Lipschitz condition. Our results extend previous results in this direction by Matkowski and Miś in [Math. Nachr. 117 (1984) 155–159] for n = 1 and the author in [Monatsh. Math. 137(2) (2002) 99–114] for n = 2 .