Generalized sharp Hardy type and Caffarelli-Kohn-Nirenberg type inequalities on Riemannian manifolds
Generalized sharp Hardy type and Caffarelli-Kohn-Nirenberg type inequalities on Riemannian manifolds
We prove generalized Hardy's type inequalities with sharp constants and Caffarelli-Kohn-Nirenberg inequalities with sharp constants on Riemannian manifolds $M$. When the manifold is Euclidean space we recapture the sharp Caffarelli-Kohn-Nirenberg inequality. By using a double limiting argument, we obtain an inequality that implies a sharp Hardy's inequality, for functions with …