A Variation of L p Uncertainty Principles in Weinstein Setting

Abstract

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 Lαp-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 Lαp versions and depend on the sets of concentration Ω and Σ, and on the time function ϕ. However, the third uncertainty principle is also Lαp version depends on the sets of concentration and he is independent on the band limited function ϕ. These Lαp-Donoho-Stark-type inequalities generalize the results obtained in the case p = q = 2.