On Fejer and Bochner-Riesz Means

Abstract

For the Fejer means on \(L_p(R), 1\le p\le\infty\) an equivalence between the rate of its convergence and an appropriate K-functional is established. For the Bochner-Riesz means on \(L_p(R^d), 1\le p\le\infty, d=1,2,\dots\) an equivalence between the rate of convergence and the corresponding K-functional is obtained. The results are of the form of strong converse inequality of type A.