Quadrature formulas with variable nodes and Jackson-Nikolskii inequalities for rational functions (Q1704131)

There are derived and investigated new parametric quadrature formulae for computing integrals on a class of complex rational functions over circles and some special intervals including the whole real axis in this paper. These results are used for deriving \((q,p)\) inequalities of Jackson-Nikolskij type. It is stated that \((\infty,2)\) and \((\infty,4)\) inequality are even sharp. The article extends known results.