Convergence of the Vallée-Poussin means for Fourier-Jaccobi sums (Q1387368)

It is known that Cesàro means of Fourier-Jacobi series are uniformly bounded as operators for \(-1/2\leq \alpha ,\beta <1/2.\) Hence, the de la Vallée-Poussin means \(V_{m,n}^{\alpha ,\beta }\) are uniformly bounded as operators for \(-1/2\leq \alpha ,\beta <1/2 \) and \(m=O(n)\), too. The main result of the paper under review is about uniform boundedness of the de la Vallée-Poussin means as operators acting in \(C[- 1,1]\) for \(a\leq m/n \leq b\), \(a>0\), and \(-1<\alpha ,\beta \leq 0\).