Is radix sort really O(n) for sorting 32 bit integers?
You can choose $k = 1$ and then the time is $\Theta(32(n+2)) = \Theta(n)$ and the space is $\Theta(2n + 2) = \Theta(n)$. In general, if you replace 32 by any fixed number, the complexities will be $\Theta(n)$. If, however, you try to use radix sort with integers of non-constant width $m$, the complexities will be as stated (with $32$ replaced by $m$), or even worse, since you are assuming that operations on these integers take constant time, which might not be the case for integers of arbitrary size (depending on your computation model).