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<p>We present a unified and concise method for establishing <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>p</mi> </msup> </math></EquationSource> <EquationSource Format="TEX">$L^{p}$</EquationSource> </InlineEquation> Hardy and Rellich inequalities for a broad class of subelliptic operators of divergence type. The approach, based on a fundamental algebraic identity, provides explicit control on maximizing sequences and yields sharp constants in several significant cases. It applies beyond the Euclidean framework, covering the Heisenberg and Carnot group settings, and extends to a variety of subelliptic operators such as the Heisenberg–Greiner and Baouendi–Grushin operators.</p>

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A unified approach to \(L^{p}\) Hardy and Rellich-type inequalities in Euclidean and non-Euclidean settings

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  • 发表日期：

    2026年2月19日

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  • Lorenzo D’Arca

摘要

We present a unified and concise method for establishing L p $L^{p}$ Hardy and Rellich inequalities for a broad class of subelliptic operators of divergence type. The approach, based on a fundamental algebraic identity, provides explicit control on maximizing sequences and yields sharp constants in several significant cases. It applies beyond the Euclidean framework, covering the Heisenberg and Carnot group settings, and extends to a variety of subelliptic operators such as the Heisenberg–Greiner and Baouendi–Grushin operators.