Approximation of periodic functions by Zygmund means
Let \(E_ p(\epsilon)=\{f\in L_ p:\) \(E_ n(f)_ p\leq \epsilon_ n\), \(n\in Z_+\}\) where \(\epsilon =\{\epsilon_ n\}\) with \(0<\epsilon_ n\downarrow 0\), and let \(H^{\ell}_ p[\omega]\{f\in L_ p:\omega_{\ell}(f,\delta)\leq \omega (\delta)\) \((\delta \downarrow +0)\}\); \(L_ p\), \(1\leq p<\infty\) the space of all measurable \(2\pi\)- periodic functions for which \(\| f\|_ p=(1/\pi \int^{2\pi}_{0}| f(x)|^ p dx)^{1/p}<\infty\), \(L_{\infty}=C\) the space of continuous functions. The author solves the problem for exact order of approximation with normal Zygmund means for the function classes \(E_ p(\epsilon)\) and \(H^{\ell}_ p[\omega]\), \(1\leq p\leq \infty\).
scientific article; zbMATH DE number 4038441