Case 2

If $-n < \la \leq 0$, then $u(0)$ may not exist, but $u(\xi)$ is locally integrable near $0$, so $\dst{u}{\phi}$ is defined. Indeed, if $B = B(0;1)$ and $1_B$ is its indicator function, and if $\sg$ denotes the usual volume form on $\bS^{n-1}$, then
$$\begin{align*} \dst{u}{1_B} &:= \int_B u(\xi) d^n\xi = \int_{\bS^{n-1}} v(\om)... ...C \int_0^1 r^{\la+n-1} dr < \infty, \word{since} \la + n - 1 > -1. \end{align*}$$