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A classical result of approximation theory states that , where is the modulus of smoothness of defined by means of the variation functional, if and only if is absolutely continuous. Such theorem is crucial in order to obtain results about convergence and order of approximation for linear and non-linear integral operators in BV-spaces. It was an open problem to extend the above result to the setting of -variation in the multidimensional frame. In this paper, working with a concept of multidimensional...
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