Multivariate Jackson Inequality

By known multivariate versions of the classical Jackson theorem, every compact cube P in R^N admits Jackson’s inequality. The purpose of this note is to deliver other examples of Jackson sets in R^N. We shall show that a finite union of disjoint Jackson compact sets in R^N is also a Jackson set and that this in general fails to hold for an infinite union of Jackson sets. We also give a characterization of Jackson sets in the family of Markov compact sets in R^N which together with a Bierstone result permits one to show that Whitney regular compact subsets of R^N are Jackson.