  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.
