Anisotropic Caffarelli-Kohn-Nirenberg inequalities with higher-order fractional derivatives

Abstract

We prove a family of anisotropic Caffarelli-Kohn-Nirenberg interpolation inequalities involving higher-order fractional derivatives and weights of the form $|x^{\prime }{|}^{{\theta }_1}|x{|}^{{\theta }_2}|x_n{|}^{{\theta }_3}$.

13 pages