Slight extensions of some theorems on the rate of pointwise approximation of functions from some subclasses of <i>L^p</i>

Abstract

In this paper we prove some results on the rate of pointwise approximation of functions by means of some matrix transformations related to the partial sums of a Fourier series, removing the assumptions that entries of the considered matrix belong to the classes RBV S or HBV S. In fact, with weaker assumptions, our results give better degrees than those obtained previously. Moreover, some results that have been obtained earlier follow from our results as special cases. Finally, we present some theorems of such type involving the so-called γRBV S or γHBV S classes of numerical sequences.