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
نویسندگان
چکیده
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.
منابع مشابه
Quasicompact and Riesz unital endomorphisms of real Lipschitz algebras of complex-valued functions
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