Suppose g = a semi-simple Lie algebra over C G = the corresponding adjoint group B = a Borel subgroup of G T = a Cartan subgroup of B b, t = corresponding Lie algebras Σ = roots corresponding to the choice of t ∆ = simple roots corresponding to the choice of b W = the Weyl groupNG(T )/T . For each α in ∆, let eα 6= 0 be an element of the root space gα. The triple (b, t, {eα}) is called a frame ...

In this work, by combining Carlson-type and Nash-type inequalities for the Weinstein transform $\mathscr{F}_W$ on $\mathbb{K}=\mathbb{R}^{d-1}\times[0,\infty)$, we show Laeng-Morpurgo-type uncertainty inequalities. We establish also local-type $\mathscr{F}_W$, deduce a Heisenberg-Pauli-Weyl-type inequality transform.

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 different weights. Furthermore, present some Heisenberg-Pauli-Weyl inequalities terms on balls centred at origin radius R in \mathbb{R} ^n $.