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In this paper, we consider the Nemytskii operator (Hf)(t) = h(t, f(t)), generated by a given function h. It is shown that if H is globally Lipschitzian and maps the space of functions of bounded (p,2,α)-variation (with respect to a weight function α) into the space of functions of bounded (q,2,α)-variation (with respect to α) 1&lt;q&lt;p, then H is of the form (Hf)(t) = A(t)f(t)+B(t). On the other hand, if 1&lt;p&lt;q then H is constant. It generalize several earlier results of this type due to Matkowski-Merentes and Merentes. Also, we will prove that if a uniformly continuous Nemytskii operator maps a space of bounded variation with weight function in the sense of Merentes into another space of the same type, its generator function is an affine function.

On the Nemytskii Operator in the Space of Functions of Bounded (p, 2, α)-Variation with Respect to the Weight Function