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Let $\nu$ be a nondecreasing concave sequence of positive real numbers and $1\leq p<\infty$. In this note, we introduce the notion of modulus of $p$-variation for a function of a real variable, and show that it serves in at least two important problems, namely, the uniform convergence of Fourier series and computation of certain $K$-functionals. Using this new tool, we first define a Banach space, denoted $V_p[\nu]$, that is a natural unification of the Wiener class $BV_p$ and the Chanturiya class $V[\nu]$. Then we prove that $V_p[\nu]$ satisfies a Helly-type selection principle which enables us to characterize continuous functions in $V_p[\nu]$ in terms of their Fej\'{e}r means. We also prove that a certain $K$-functional for the couple $(C,BV_p)$ can be expressed in terms of the modulus of $p$-variation, where $C$ denotes the space of continuous functions. Next, we obtain equivalent optimal conditions for the uniform convergence of the Fourier series of all functions in each of the classes $C\cap V_p[\nu]$ and $H^\omega\cap V_p[\nu]$, where $\omega$ is a modulus of continuity and $H^\omega$ denotes its associated Lipschitz class. Finally, we establish sharp embeddings into $V_p[\nu]$ of various spaces of functions of generalized bounded variation. As a by-product of these latter results, we infer embedding results for certain symmetric sequence spaces.
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