Rajendra G. Vyas

A Note on Fourier Coefficients of Functions of Generalized Wiener Class

Let $f$ denote a $2\pi$ periodic function in $L[0,2\pi$], and $\hat{f}(n)$, $n\in Z$, be its Fourier coefficients. For a function $f$ of the generalized Wiener class $\bigwedge \BV(p(n) \uparrow\infty$) we have proved that
$$\hat{f}(n)=O\bigg(1/\Big(\sum_{i=1}^{| n|}\frac{1}{\lambda_{i}}\Big)^{1/p(k(n))}\bigg).$$

Fourier coefficients, generalized Wiener class, $p$-$\bigwedge$-bounded variation.

MSC 2000: 42A16