Pointwise strong approximation of almost periodic functions in S^1
We consider the class GM(2b) in pointwise estimate of the deviations in strong mean of S^1 almost periodic functions from matrix means of partial sums of their Fourier series.
Trigonometric series with general monotone coefficients
We study trigonometric series with general monotone coefficients. Convergence results in the different metrics are obtained. Also, we prove a Hardy-type result on the behavior of the series near the origin.
On Generalized Lipschitz Classes and Fourier Series
In 1967 R.P. Boas Jr. found necessary and sufficient conditions of belonging of a function to a Lipschitz class. Later Boas’s findings were generalized by many authors (M. and S. Izumi (1969), L.-Y. Chan (1991) and others). Recently, L. Leindler (2000) and J. Nemeth (2001) have published two papers, in which they have generalized all the previous results. The authors have considered the case, when the order of modulus of smoothness equals one (L. Leindler) or two (J. Nemeth). In this paper, we prove theorems of Boas-type for the modulus of smoothness of any order. Furthermore, we solve the inverse problem. Also, we discuss some conditions on a majorant which are equivalent to the well-known conditions of Bari-Stechkin.