Hardy–Sobolev–Rellich, Hardy–Littlewood–Sobolev and Caffarelli–Kohn–Nirenberg Inequalities on General Lie Groups

Key Points

• Various geometrical inequalities are established, including Hardy and Sobolev inequalities for general Lie groups.
• The critical versions of inequalities, such as Hardy–Littlewood–Sobolev and Caffarelli–Kohn–Nirenberg, are included.
• Assessment involves sub-elliptic differential operators in both unimodular and non-unimodular cases, across compact and noncompact settings. ','These findings deepen the understanding of inequalities, implying potential applications in mathematical physics and analysis.