A Review on Approximation Results for Integral Operators in the Space of Functions of Bounded Variation

الملخص EN

We present a review on recent approximation results in the space of functions of bounded variation for some classes of integral operators in the multidimensional setting.

In particular, we present estimates and convergence in variation results for both convolution and Mellin integral operators with respect to the Tonelli variation.

Results with respect to a multidimensional concept of φ -variation in the sense of Tonelli are also presented.