On functions of bounded $p$-variation

B. I. Golubov

Izvestiya. Mathematics , Tome 2 (1968) no. 4, pp. 799-819

Résumé

In this article we obtain an asymptotic formula for the approximations to functions in the class $V_p^\alpha$ ($0\leqslant\alpha\infty$, $1\leqslant p\infty$) by Fourier sums in the metric of $L^p $ ($1\leqslant p$). We find sufficient conditions and also criteria for the continuity of the derivative $f^\alpha(t)$ of a function in the class $V_p^\alpha$. We also give some results on the Fourier coefficients of functions in the above class.