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Sharp estimates of the potential kernel for the harmonic oscillator with applications

Published online by Cambridge University Press:  11 January 2016

Adam Nowak  and
Krzysztof Stempak
Adam Nowak
Affiliation:
Instytut Matematyczny Polska Akademia Nauk, Sniadeckich 8, 00-956 Warszawa, Poland, Adam.Nowak@impan.pl
Krzysztof Stempak
Affiliation:
Instytut Matematyki i Informatyki, Politechnika Wrocławska, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland, and Katedra Matematyki i Zastosowań Informatyki, Politechnika Opolska, Mikołajczyka 5, 45-271 Opole, Poland, Krzysztof.Stempak@pwr.wroc.pl
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Abstract

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We prove qualitatively sharp estimates of the potential kernel for the harmonic oscillator. These bounds are then used to show that the Lp–Lq estimates of the associated potential operator obtained recently by Bongioanni and Torrea are in fact sharp.

Keywords

47G4031C15
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 212 , December 2013 , pp. 1 - 17
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2013

References

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