On the weighted exponential approximations (Q1343488)

The author investigates the approximation properties of singular integrals \[ \gamma^{-1}_{\sigma, r} \int^ \infty_{-\infty} f(u) g_{\sigma,r}(z- u) du, \] where \(z= x+ iy\), \(f\) is a measurable complex- valued function with \[ \int^ \infty_{- \infty} {| f(u)|\over 1+ u^{2r}} du< \infty,\;g_{\sigma, r}(z):= \left({1\over z}\sin{\sigma z\over 2r}\right)^{2r}\text{ and }\gamma_{\sigma, r}:= \int^ \infty_{- \infty} g_{\sigma, r} (t) dt. \] {}.