On Nemytskii operator in the space of set-valued functions of bounded p-variation in the sense of Riesz with respect to the weight function
2013
artykuł naukowy
angielski
- variation in the sense of Riesz
- set-valued functions
- weight function
- composition operator
- Jensen equation
EN In this paper we consider the Nemytskii operator (Hf) (t) = h(t, f (t)), generated by a given set-valued function h is considered. It is shown that if H is globally Lipschitzian and maps the space of functions of bounded p-variation (with respect to a weight function α) into the space of set-valued functions of bounded q-variation (with respect to α) ) 1 < q < p, then H is of the form (Hφ)(t) = A(t)φ(t) + B(t). On the other hand, if 1 < p < q, then H is constant. It generalizes many earlier results of this type due to Chistyakov, Matkowski, Merentes-Nikodem, Merentes-Rivas, Smajdor-Smajdor and Zawadzka.
17 - 32
CC BY-NC-ND (uznanie autorstwa - użycie niekomercyjne - bez utworów zależnych)
publiczny
10