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

On general Caffarelli-Kohn-Nirenberg type inequalities involving non-doubling weights