Hardy-Littlewood-Sobolev Type Inequality and Stein-Wiess Type Inequality on Carnot Groups

2013/03/21 by Tingxi Hu, Hu, Tingxi, Pengcheng Niu +1
Mathematics · #Advanced Harmonic Analysis Research #Nonlinear Partial Differential Equations #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.1303.5185

Abstract

A Stein-Weiss type inequality on Carnot groups is established by proving the boundedness of an integral operator and the Hardy-Littlewood-Sobolev type inequality on Carnot groups is also derived.

Related

• Existence of optimizers of the Stein-Weiss inequalities on Carnot groups
• Hardy, Rellich and Uncertainty principle inequalities on Carnot Groups
• Sharp Hardy type inequalities on the Carnot Group
• Hardy-Littlewood-Sobolev and Stein-Weiss inequalities on homogeneous Lie groups
• Reverse Stein-Weiss, Hardy-Littlewood-Sobolev, Hardy, Sobolev and Caffarelli-Kohn-Nirenberg inequalities on homogeneous groups