Acta Mathematica Vietnamica
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Stability Estimates for the Heisenberg Uncertainty Principle with Dunkl Weights
Nguyen Tuan Duy , Nguyen Van Phong , Lam Thi Bich Thuypp. 449-462
Abstract
We study the stability of the Heisenberg Uncertainty Principle with Dunkl weights, inspired by recent progress on stability in functional and geometric inequalities. First, using the Bakry-Émery $\varGamma _2$-calculus, we establish several versions of the Poincaré inequality for measures involving Dunkl-Gaussian weights. We then prove a Heisenberg-type uncertainty principle adapted to Dunkl weights through suitable identities. By combining these results, we obtain several stability estimates for the Dunkl-weighted Heisenberg uncertainty principle. Our work extends existing methods developed for monomial weights to the more complex Dunkl setting.