Improved Caffarelli-Kohn-Nirenb erg inequalities in unit ball and sharp constants in dimension three

We show that the Caffarelli-Kohn-Nirenb erg inequalities in unit ball Bn can be improved by subtraction of Hardy term. In three dimension and 0 & LE; a < 21, we show that the sharp constant coincides with that in R3. This is an analogous result to that of the sharp constant in the n-1 2-th order Hardy-Sobolev-Maz'ya inequality in the unit ball of dimension n when n is odd. As an application, we obtain a sharp Sobolev inequality on hyperbolic Caffarelli-Kohn-Nirenb erg space introduced by L. Dupaigne, I. Gentil and S. Zugmeyer. & COPY; 2023 Elsevier Ltd. All rights reserved.