On a norm and approximate characteristics of classes of multivariable functions

We introduce a space of quasicontinuous functions and study its approximate characteristics, i.e., ε-entropy and widths. We establish inequalities for norms of trigonometric polynomials in this space. In addition, we obtain exponents of the ε-entropy and widths of some classes of functions with low smoothness. __________ Translated from Sovremennaya Matematika. Fundamental'nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 25, Theory of Functions, 2007.