Multivariate Jackson Inequality

By known multivariate versions of the classical Jackson theorem, every compact cube PP in RNRN admits Jackson’s inequality. The purpose of this note is to deliver other examples of Jackson sets in RNRN. We shall show that a finite union of disjoint Jackson compact sets in RNRN 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 RNRN which together with a Bierstone result permits one to show that Whitney regular compact subsets of RNRN are Jackson.