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Anisotropic Hardy inequalities

Part of: Inequalities

Published online by Cambridge University Press:  20 December 2017

Francesco Della Pietra ,
Giuseppina di Blasio  and
Nunzia Gavitone
Francesco Della Pietra
Affiliation:
Università degli studi di Napoli Federico II, Dipartimento di Matematica e Applicazioni ‘R. Caccioppoli’, Via Cintia, Monte S. Angelo – 80126 Napoli, Italia (f.dellapietra@unina.it)
Giuseppina di Blasio
Affiliation:
Università degli studi della Campania ‘L. Vanvitelli’, Dipartimento di Matematica e Fisica, Viale Lincoln, 5 – 81100 Caserta, Italia (giuseppina.diblasio@unicampania.it)
Nunzia Gavitone
Affiliation:
Università degli studi di Napoli Federico II, Dipartimento di Matematica e Applicazioni ‘R. Caccioppoli’, Via Cintia, Monte S. Angelo – 80126 Napoli, Italia (nunzia.gavitone@unina.it)
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Abstract

We study some Hardy-type inequalities involving a general norm in ℝn and an anisotropic distance function to the boundary. The case of the optimality of the constants is also addressed.

Keywords

Hardy inequalitiesanisotropic operatorsoptimal constants

MSC classification

Secondary: 26D10: Inequalities involving derivatives and differential and integral operators 26D15: Inequalities for sums, series and integrals
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 148 , Issue 3 , June 2018 , pp. 483 - 498
Copyright
Copyright © Royal Society of Edinburgh 2018 

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