Tohoku Mathematical Journal
2020
December
SECOND SERIES VOL. 72, NO. 4

Tohoku Math. J.
72 (2020), 569-579

Title STRUCTURE OF MINIMIZERS OF CAFARELLI-KOHN-NIRENBERG INEQUALITY

Author Jingshi Xu

(Received November 6, 2018, revised September 9, 2019)
Abstract. In this paper we generalize the characterization for Sobolev spaces with constant exponent via averages on balls to the variable exponent setting. This method can be used to define Sobolev spaces with variable exponent on metric spaces.

Mathematics Subject Classification. Primary 46E35; Secondary 42B25, 42B35.
Key words and phrases. Variable exponent, Sobolev space, average on ball, Hörmander's conditions.

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