| Abstract: |
| The Moser--Trudinger inequality is considered as a limiting case of the Sobolev inequality in the framework of Orlicz spaces. However, the Moser--Trudinger inequality is not obtained via a direct limiting procedure for the Sobolev inequality. In this talk, we consider a Sobolev type inequality and we show that the Carleson--Chang limit on the Moser--Trudinger inequality is derived as a limit of the concentration level of the Sobolev type inequality. In addition to the property, we study the variational problem on the inequality. |
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