  The Weinstein operator has several applications in pure and applied
Mathematics especially in Fluid Mechanics and satisfies some uncertainty
principles similar to the Euclidean Fourier transform. The aim of this paper is
establish a generalization of uncertainty principles for Weinstein transform in
$L_\alpha^p$-norm. Firstly, we extend the Heisenberg-Pauli-Weyl uncertainty
principle to more general case. Then we establish three continuous uncertainty
principles of concentration type. The first and the second uncertainty
principles are $L_\alpha^p$ versions and depend on the sets of concentration
$\Omega$ and $\Sigma$, and on the time function $\varphi$. However, the third
uncertainty principle is also $L_\alpha^p$ version depends on the sets of
concentration and he is independent on the band limited function $\varphi$.
These $L_\alpha^p$-Donoho-Stark-type inequalities generalize the results
obtained in the case $p=q=2$.
