  We will establish the Caffarelli-Kohn-Nirenberg type inequalities with
non-doubling weights being permitted. The classical Caffarelli-Kohn-Nirenberg
type inequalities are categorized into non-critical and critical cases,
  and it is known that there is some kind of mysterious relationship between
them. Interestingly the new framework in this treatise allows them to be
integrated and reveals the meaning of mysterious relationships.
