On the \(L_{p}\)-saturation of the Ye-Zhou operator

Abstract

We solve the saturation problem for a class of Ye-Zhou operator \(T_{n}( f , x ) = P_{n}( x ) A_{n} L_{n}( f )\) with suitable sequence of matrices \(\{ A_{n} \}_{n \geq 1}.\) The solution is based on the saturation theorem for the Kantorovich operator established by V. Maier and S. D. Riemenschneider.