\(L^p\)-norms of periodizations over integer lattices
The periodizations with respect to a rotated integer lattice \(g_\rho (x)=\sum_{\nu \in \mathbb{Z}^d}f(\rho (x-\nu ))\) corresponding to \(\rho\in \text{SO}(d)\) of the functions \(f\in L^1(\mathbb{R}^d)\) appear in the Steinhaus tiling set problem. In this note the author presents an estimate concerning the mixed norm \(\| g\|_{p,s}=\left( \int_{\rho \in\text{SO}(d)}\| g_\rho -\hat g(0) \|_p^s\, d\rho \right)^{1/s}\).
scientific article; zbMATH DE number 5960930