In this paper we present the notion of the space of bounded p(·)-variation in the sense of Wiener-Korenblum with variable exponent. We prove some properties of this space and we show that the composition operator...In this paper we present the notion of the space of bounded p(·)-variation in the sense of Wiener-Korenblum with variable exponent. We prove some properties of this space and we show that the composition operator H, associated with , maps the into itself, if and only if h is locally Lipschitz. Also, we prove that if the composition operator generated by maps this space into itself and is uniformly bounded, then the regularization of h is affine in the second variable, i.e. satisfies the Matkowski’s weak condition.展开更多
文摘In this paper we present the notion of the space of bounded p(·)-variation in the sense of Wiener-Korenblum with variable exponent. We prove some properties of this space and we show that the composition operator H, associated with , maps the into itself, if and only if h is locally Lipschitz. Also, we prove that if the composition operator generated by maps this space into itself and is uniformly bounded, then the regularization of h is affine in the second variable, i.e. satisfies the Matkowski’s weak condition.
