Hardy-Littlewood-Sobolev Type Inequality and Stein-Wiess Type Inequality on Carnot Groups
Tingxi Hu, Pengcheng Niu
TL;DR
This paper establishes a Stein-Weiss type inequality and a Hardy-Littlewood-Sobolev type inequality on Carnot groups by proving the boundedness of related integral operators.
Contribution
It introduces new inequalities on Carnot groups, extending classical results to a non-commutative geometric setting.
Findings
Proved boundedness of an integral operator on Carnot groups.
Derived Hardy-Littlewood-Sobolev type inequality for Carnot groups.
Established Stein-Weiss type inequality in the same setting.
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.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Nonlinear Partial Differential Equations · Geometric Analysis and Curvature Flows