Annals of Functional Analysis

A note on stability of Hardy inequalities

Michael Ruzhansky and Durvudkhan Suragan

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In this note, we formulate recent stability results for Hardy inequalities in the language of Folland and Stein’s homogeneous groups. Consequently, we obtain remainder estimates for Rellich-type inequalities on homogeneous groups. Main differences from the Euclidean results are that the obtained stability estimates hold for any homogeneous quasinorm.

Article information

Ann. Funct. Anal., Volume 9, Number 4 (2018), 451-462.

Received: 16 August 2017
Accepted: 12 October 2017
First available in Project Euclid: 15 June 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Primary: 22E30: Analysis on real and complex Lie groups [See also 33C80, 43-XX]
Secondary: 43A80: Analysis on other specific Lie groups [See also 22Exx]

Hardy inequality Rellich inequality stability remainder term homogeneous Lie group


Ruzhansky, Michael; Suragan, Durvudkhan. A note on stability of Hardy inequalities. Ann. Funct. Anal. 9 (2018), no. 4, 451--462. doi:10.1215/20088752-2017-0060.

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