  We develop a regularization operator based on smoothing on a locally defined
length scale. This operator is defined on $L_1$ and has approximation
properties that are given by the local regularity of the function it is applied
to and the local length scale. Additionally, the regularized function satisfies
inverse estimates commensurate with the approximation orders. By combining this
operator with a classical hp-interpolation operator, we obtain an hp-Cl\'ement
type quasi-interpolation operator, i.e., an operator that requires minimal
smoothness of the function to be approximated but has the expected
approximation properties in terms of the local mesh size and polynomial degree.
As a second application, we consider residual error estimates in hp-boundary
element methods that are explicit in the local mesh size and the local
approximation order.
