Torus homeomorphisms, Fourier coefficients, and integral smoothness (Q1333681)

The decrease rate of Fourier coefficients of the composition \(f\circ h\), where \(f\in C(T^ n)\) and \(h\) is a homeomorphism of the torus \(T^ n\) is investigated. An estimate of the integral smoothness, which can be attained by means of a torus homeomorphism, is given. The results are consequences of a general theorem on reducibility of compacts in the space of continuous functions into certain functional classes by means of synchronous change of variables.