A Sobolev Orthogonal System of Functions Generated by a Walsh System

Properties of functions from the Sobolev orthogonal system $\mathfrak W_r$ generated by the Walsh system are studied. In particular, recurrence relations for functions from $\mathfrak W_1$ are obtained. The uniform convergence of Fourier series in the system $\mathfrak W_r$ to functions $f$ from the Sobolev spaces $W^r_{L^p}$, $p\ge 1$, $r=1,2,\dots$ is proved.