Some results on double Fourier-Stieltjes transform (Q910994)

For functions of bounded variation in the sense of Hardy and Krause in \(R\times R\), some results on the double Fourier-Stieltjes transform are obtained. The main result is the inequality \[ \begin{multlined} \int^{\infty,\infty}_{-\infty,-\infty} | \int^{\infty,\infty}_{-\infty,-\infty} \frac{\sin su}{s} \frac{\sin tv}{t} dg(u,v) |^2 ds dt\leq \\ \leq \int^{\infty,\infty}_{-\infty,-\infty} | \int^{\infty,\infty}_{-\infty,-\infty} \frac{e^{-i(su+tv)}} {st} dg(u,v) |^2 ds dt, \end{multlined} \] useful in the study of trigonometric series.