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- W2950907477 abstract "In this paper we obtain an inequality on the unit disc $B$ in the plane, which improves the classical Moser-Trudinger inequality and the classical Hardy inequality at the same time. Namely, there exists a constant $C_0>0$ such that [ int_B e^{frac {4pi u^2}{H(u)}} dx le C_0 < infty, quad forall; uin C^infty_0(B),] where $$H(u) := int_B |n u|^2 dx - int_B frac {u^2}{(1-|x|^2)^2} dx.$$ This inequality is a two dimensional analog of the Hardy-Sobolev-Maz'ya inequality in higher dimensions, which was recently intensively studied. We also prove that the supremum is achieved in a suitable function space, which is an analog of the celebrated result of Carleson-Chang for the Moser-Trudinger inequality." @default.
- W2950907477 created "2019-06-27" @default.
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- W2950907477 date "2010-12-27" @default.
- W2950907477 modified "2023-10-16" @default.
- W2950907477 title "A Hardy-Moser-Trudinger inequality" @default.
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- W2950907477 doi "https://doi.org/10.48550/arxiv.1012.5591" @default.
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