A Hardy-Moser-Trudinger inequality

Guofang Wang; Dong Ye

doi:10.1016/j.aim.2011.12.001

A Hardy-Moser-Trudinger inequality

Guofang Wang^*
, Dong Ye

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

74 Scopus citations

Abstract

In this paper we obtain an inequality on the unit disk B in R2, 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 This inequality is a two-dimensional analog of the Hardy-Sobolev-Maz'ya inequality in higher dimensions, which has been intensively studied recently. 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.

Original language	English
Pages (from-to)	294-320
Number of pages	27
Journal	Advances in Mathematics
Volume	230
Issue number	1
DOIs	https://doi.org/10.1016/j.aim.2011.12.001
State	Published - 1 May 2012
Externally published	Yes

Keywords

Extremal
Hardy inequality
Hardy-Moser-Trudinger inequality
Moser-Trudinger inequality

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10.1016/j.aim.2011.12.001

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AB - In this paper we obtain an inequality on the unit disk B in R2, 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 This inequality is a two-dimensional analog of the Hardy-Sobolev-Maz'ya inequality in higher dimensions, which has been intensively studied recently. 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.

KW - Extremal

KW - Hardy inequality

KW - Hardy-Moser-Trudinger inequality

KW - Moser-Trudinger inequality

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DO - 10.1016/j.aim.2011.12.001

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JO - Advances in Mathematics

JF - Advances in Mathematics

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A Hardy-Moser-Trudinger inequality

Abstract

Keywords

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