Criteria for a Function to Belong to the $p$-Variational Besov Space

Necessary and sufficient conditions for a function to belong to the Besov space constructed from the space $V_p$ of functions of bounded $p$-variation are studied. These conditions are expressed in terms of approximations of functions by Fourier partial sums and Fejér means, as well as in terms of the norms of the derivatives of the approximating polynomials in $V_p$.