Sharp Hardy–Littlewood–Sobolev Inequality on the Upper Half Space

Jingbo Dou, Mei‐Jun Zhu

Type: Article

Publication Date: 2013-10-16

Citations: 74

DOI: https://doi.org/10.1093/imrn/rnt213

Abstract

The sharp Hardy–Littlewood–Sobolev inequality on the upper half space is proved. The existences of extremal functions are obtained. For certain exponent, we classify all extremal functions via the method of moving sphere, and compute the best constants for the sharp inequality.

Locations

International Mathematics Research Notices - View
arXiv (Cornell University) - View - PDF

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+	Singular Integrals and Differentiability Properties of Functions.	1971	Elias M. Stein
+	Convolution operators and L(p,q) spaces	1963	Richard O’Neil
+	Second Order Elliptic Equations and Elliptic Systems	1998	Chen Ya-zhe Lan-Cheng Wu
+ PDF Chat	The Yamabe problem on manifolds with boundary	1992	José F. Escobar
+	Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation	1977	Élliott H. Lieb
+	Super Polyharmonic Property of Solutions for PDE Systems and Its Applications	2011	Wenxiong Chen Congming Li
+	The two dimensional<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:math>Minkowski problem and nonlinear equations with negative exponents	2012	Jingbo Dou Mei‐Jun Zhu
+	Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities	2002	Élliott H. Lieb
+	Uniqueness theorems through the method of moving spheres	1995	Yanyan Li Mei‐Jun Zhu
+	Sharp Sobolev Inequalities on the Sphere and the Moser--Trudinger Inequality	1993	William Beckner