  In this paper, we establish a general weighted Hardy type inequality for the
$% p-$Laplace operator with Robin boundary condition. We provide various
concrete examples to illustrate our results for different weights. Furthermore,
we present some Heisenberg-Pauli-Weyl type inequalities with boundary terms on
balls with radius $R$ at the origin in $\mathbb{R}^n$.

Analysis of PDEs;Functional Analysis