2 research outputs found
On approximations by trigonometric polynomials of classes of functions defined by moduli of smoothness
In this paper, we give a characterization of Nikol'ski\u{\i}-Besov type
classes of functions, given by integral representations of moduli of
smoothness, in terms of series over the moduli of smoothness. Also, necessary
and sufficient conditions in terms of monotone or lacunary Fourier coefficients
for a function to belong to a such a class are given. In order to prove our
results, we make use of certain recent reverse Copson- and Leindler-type
inequalities.Comment: 18 pages. arXiv admin note: substantial text overlap with
arXiv:1208.612
On Approximations by Trigonometric Polynomials of Classes of Functions Defined by Moduli of Smoothness
In this paper, we give a characterization of Nikol'skiȋ-Besov type classes of functions, given by integral representations of moduli of smoothness, in terms of series over the moduli of smoothness. Also, necessary and sufficient conditions in terms of monotone or lacunary Fourier coefficients for a function to belong to such a class are given. In order to prove our results, we make use of certain recent reverse Copson-type and Leindler-type inequalities