Fourier transform and continuity of functions of bounded $\Phi$-variation

In this paper, we prove several criteria for the continuity of functions of bounded $\Phi$-variation that belong to the spaces $L^q$ on $\mathbb{R}$. The first result connects the continuity of a function with the behaviour of its Fourier transform, the second result is based on the notion of the modulus of continuity in $\Psi(L)$, and the third result concerns the degree of approximation by partial Fourier integrals. Theorems 1 and 3 in the case $\Phi(u)=|u|^p$, $1\le p<\infty$, were obtained earlier by the first author.