Local approximation operators on box meshes

This paper analyzes the approximation properties of spaces of piece-wise tensor product polynomials over box meshes with a focus on application to IsoGeometric Analysis (IGA). The errors are measured in Lebesgue norms. Estimates of different types are considered: local and global, with full or reduced Sobolev seminorms. Attention is also paid to the dependence on the degree and exponential convergence is proved for the approximation of analytic functions.