Approximation properties of partial Fourier sums in the $p$-variation metric

In this paper, we examine the degree of approximation by Fourier partial sums in the $p$-variational norm. We propose two criteria for convergence of these sums with a given rate in terms of growth of the norms of the differentiated Fourier partial sums. Also, we establish the relationship between the approximation of a function and its conjugate function.