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We characterize the set of all functions f of R to itself such that the associated superposition operator T: g → f º g maps the class BV
(R) into itself. Here BV
(R), 1 ≤ p < ∞, denotes the set of primitives of functions of bounded p-variation, endowed with a suitable norm. It turns out that such an operator is always bounded and sublinear. Also, consequences for the boundedness of superposition operators defined on Besov spaces B
are discussed....
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