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We establish the full range of the Caffarelli-Kohn-Nirenberg inequalities forradial functions in the Sobolev and the fractional Sobolev spaces of order $0 <s \le 1$. In particular, we show that the range of the parameters for radialfunctions is strictly larger than the one without symmetric assumption.Previous known results reveal only some special ranges of parameters even inthe case $s=1$. Our proof is new and can be easily adapted to other contexts.Applications on compact embeddings are also mentioned.

The Caffarelli-Kohn-Nirenberg Inequalities For Radial Functions