Optimal quadrature formulas for functions belonging to a weight class (Q1814468)

In the paper there are studied properties of the optimal quadrature rules corresponding to the following problem \(R(I)=\sup\{|\int_ \Omega f(t)dt-I(f)|\): \(\| f\|_ k\leq 1\}\), \(\| f\|_ k=(\int_ \Omega(| f'|^ p+| vf|^ p)dt)^{1/p}\), \(I(F)=\sum_{j=1}^ K {\mathcal C}_ j f(x_ j)\) where \(\Omega\subset\mathbb{R}\) is an open set, \(C_ 0^ 1(\Omega)\) is the space of continuously differentiable functions in \(\Omega\), \(1<p<\infty\), \(v\in L_{\text{loc}}^ p(\Omega)\), \(W\) is a completion of \(C_ 0^ 1(\Omega)\).