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On characterization of the Lipschitzian composition operator between spaces of functions of bounded \(p\)-variation. (English) Zbl 0856.47042

The authors prove that the Nemytskij operator \(Fu(t)= f(t, u(t))\) satisfies a global Lipschitz condition between the spaces \(RV_p[a, b]\) and \(RV_q[a, b]\) \((1\leq q\leq p)\) if and only if \(f\) is linear in the second variable. The case \(p= q\) was previously considered by the first author in Ann. Univ. Sci. Budapest Rolando Eötvös, Sect. Math. 34, 139-144 (1991; Zbl 0808.47050).

MSC:

47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.)

Citations:

Zbl 0808.47050
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References:

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