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A Characterization of a Modulus of Smoothness in Multidimensional Setting

Laura Angeloni — 2011

Bollettino dell'Unione Matematica Italiana

A classical result of approximation theory states that lim δ 0 ω ( f , δ ) = 0 , where ω is the modulus of smoothness of f defined by means of the variation functional, if and only if f 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 φ -variation in the multidimensional frame. In this paper, working with a concept of multidimensional...

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