We show that, on the Fourier side, the sharp second order Heisenberg Uncertainty Principle (HUP) and its sharp stability for functions are nothing but the first order $L^{2}$-Caffarelli--Kohn--Nirenberg inequality and its sharp stability, applied to their Fourier transforms. This gives a proof in a few lines of the sha...
We study the sharp $L^2$-Poincar\'e inequalities on Euclidean balls and with respect to the Gaussian measure, and we focus on their stability. In both settings, the sharp constant is the first nonzero eigenvalue of a self-adjoint operator and the set of optimizers is a finite dimensional linear space. Using the spectra...
It was known that the Gaussian measures with monomial weights satisfy the sharp pointwise curvature-dimension condition $CD(1, \infty)$, and consequently they allow us to derive the sharp constant $1$ for the Poincar\'e inequality only with partial monomial weights. In this paper, we first establish the Gaussian measur...
Though the sharp $L^{2}$-Caffarelli--Kohn--Nirenberg (CKN) inequalities have been extensively studied in the entire Euclidean spaces, the corresponding problem on domains whose boundary contains the origin remains largely unexplored. We investigate the sharp $L^{2}$-CKN inequalities on half-spaces and orthants $\mathbb...
L. Nguyen, Yukta Lodha, Guo-Zhen Lu et al.· 4 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
