Critical Caffarelli-Kohn-Nirenberg inequalities via nonlinear scaling argument

Abstract

We show functional inequalities with logarithmic weights as a critical case of Caffarelli-Kohn-Nirenberg inequalities. Original CKN inequalities have polynomial weights and are shown via scaling argument. In this paper, we develop this argument into it for nonlinear scaling. Our inequalities are generalizations of critical Hardy type inequalities.

arXiv comment32 papes