Extremizer Stability of Higher-order Hardy-Rellich inequalities for Baouendi--Grushin vector fields

2025/04/28 by Avas Banerjee, Riju Basak, Banerjee, Avas +3 · 1 citation
Mathematics · #math.AP #math.CA #math.FA

paper · pdf · doi:10.1007/s12220-026-02550-6

Abstract

In this paper, we improve the L^p-Rellich and Hardy-Rellich inequalities in the setting of radial Baouendi-Grushin vector fields. We establish an identity relating the subcritical and critical Hardy inequalities, thereby demonstrating their equivalence. Moreover, we obtain improved versions of these inequalities via an analysis of extremizer stability. In the higher-order setting, we derive Hardy-Rellich type inequalities involving all radial operators in the Grushin framework and prove that all resulting constants are sharp. Finally, for the L²-higher-order cases, we compute exact remainder terms by establishing identities rather than inequalities.

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• Sharp remainder terms and stability of weighted Hardy-Poincaré and Heisenberg-Pauli-Weyl inequalities related to the Baouendi-Grushin operator

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