On multiple Fourier coefficients of a function of the generalized Wiener class

In this paper, we estimate the order of magnitude of the double Fourier coefficients of a function of the class

Properties of Functions in the Wiener ClassBVp[a,b]for0

We will investigate properties of functions in the Wiener classBVp[a,b]with0<p<1. We prove that any function inBVp[a,b] (0<p<1)can be expressed as the difference of two increasing functions inBVp[a,b]. We also obtain the explicit form of functions inBVp[a,b]and show that their derivatives are equal to zero a.e. on[a,b].

On Fourier Coefficients of Functions of Generalized Wiener Class

For the Fourier coefficients of the generalized Wiener class BV(p(n) ↑ ∞), the precise order , where k(n) is an integer for which 1 + log2 n < k(n) ≤ 2 + log2 n, is established. A problem concerning the number of Fourier coefficients having exactly the order is studied.