Bogdan Szal
Trigonometric approximation by N\"orlund type means in $L^p$-norm

Comment.Math.Univ.Carolin. 50,4 (2009) 575-589.

Abstract:We show that the same degree of approximation as in the theorems proved by L.~Leindler [{\it Trigonometric approximation in $L^p$-norm\/}, J. Math. Anal. Appl. {\bf 302} (2005), 129--136] and P.~Chandra [{\it Trigonometric approximation of functions in $L^p$-norm\/}, J. Math. Anal. Appl. {\bf 275} (2002), 13--26] is valid for a more general class of lower triangular matrices. We also prove that these theorems are true under weakened assumptions.

Keywords: class $\operatorname{Lip} (\alpha ,p)$, trigonometric approximation, $L^p$-norm
AMS Subject Classification: 42A10 41A25