Fourier Series Approximation in Besov Spaces

Defined on the top of classical $L^p$ -spaces, the Besov spaces of periodic functions are good at encoding the smoothness properties of their elements. These spaces are also characterized in terms of summability conditions on the coefficients in trigonometric series expansions of their elements. In this paper, we study the approximation properties of $2\pi$ -periodic functions in a Besov space under a norm involving the seminorm associated with the space. To achieve our results, we use a summability method presented by a lower triangular matrix with monotonic rows.