On matrix summation methods in \(L_ p\)
Let \(\{\lambda^{(n)}_\nu\}\) \((\nu= 0,\dots, n;\;n= 0,1,\dots)\) be convex downwards with respect to the index \(\nu\) and such that \(\lambda^{(n)}_\nu\to 1\) \((n\to \infty)\). A general deviation bound of the operator \[ U_n(f, \Lambda, x)= {a_0\over 2}+ \sum^n_{\nu= 1} \lambda^{(n)}_\nu(a_\nu\cos \nu x+ b_\nu\sin \nu x) \] from the generating function \(f(x)\in L_p\) \((1\leq p\leq \infty)\) is obtained.
scientific article; zbMATH DE number 795605