On the expansion with respect to Steklov means of the second differences of functions (Q1271981)

The Steklov means of a function \(f:{\mathbb R}^n\to{\mathbb R}\) is the average over a cube in \({\mathbb R}^n\) with side \(h\). This paper gives an expansion of such a function in terms of Steklov means of second (forward) differences of that function where the Steklov means are computed over cubes whose sides are geometrically decreasing. If \(f\in L_p\) on a compact set, then it is proved that convergence of the series holds in the \(L_p\) norm.