In this paper, we introduce and study a new multidimensional generalization in the sense of Tonelli of the Riesz–Medvedev $$\varphi $$ φ -variation, proving in particular a multidimensional generalization of the Riesz–Medvedev theorem. We finally discuss an application of such concept of variation to some approximation problems: in particular, we obtain some estimates and convergence results by means of convolution integral operators in the space of functions of bounded $$\varphi $$ φ -variation.
Mediterranean Journal of Mathematics – Springer Journals
Published: Jun 13, 2017
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