Suppose we try to define a convolution operator with kernel $K(x) = (1+|x|^2)^\frac{n}{2}$.
For any measurable function $f$ we define
$T[f](x) = \int_{\mathbb R^n} f(x-y) (1+|x|^2)^\frac{n}{2} dy$
It is clear that this a bounded mapping $T : L^1(\mathbb R^n) \rightarrow L^\infty(\mathbb R^n)$. The kernel also happens to be a tempered distribution.
For which exponents $1 \leq p, q \leq \infty$ is this a bounded mapping $T : L^p(\mathbb R^n) \rightarrow L^q(\mathbb R^n)$.