Annals of Functional Analysis

A note on stability of Hardy inequalities

Michael Ruzhansky and Durvudkhan Suragan

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.afa/1529028135

Digital Object Identifier
doi:10.1215/20088752-2017-0060

Mathematical Reviews number (MathSciNet)
MR3871906

Subjects
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]

Keywords
Hardy inequality Rellich inequality stability remainder term homogeneous Lie group

Citation

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. https://projecteuclid.org/euclid.afa/1529028135


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