In this paper, we investigate entropy numbers of multiplier operators of functions defined on the d-dimensional torus. In the first part, upper and lower bounds are established for entropy numbers of general multiplier operators bounded from Lp to Lq. In the second part, we apply these results to study entropy numbers of sets of finitely differentiable functions, in particular Sobolev classes, and sets of infinitely differentiable and analytic functions, on the d-dimensional torus. We prove that, the estimates for the entropy numbers are order sharp in various important situations.
R. L. B. Stabile, S. A. Tozoni