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SCHRÖDINGER OPERATORS AND THE KATO SQUARE ROOT PROBLEM

Part of: Harmonic analysis in several variables Elliptic equations and systems

Published online by Cambridge University Press:  18 December 2020

JULIAN BAILEY Open the ORCID record for JULIAN BAILEY [Opens in a new window]
JULIAN BAILEY*
Affiliation:
Mathematical Sciences Institute, Australian National University, Canberra, ACT0200, Australia
*
e-mail: [email protected]
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Abstract

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Keywords

Kato square root problemSchrödinger operatorsweighted theory

MSC classification

Primary: 42B37: Harmonic analysis and PDE
Secondary: 35J10: Schrödinger operator
Type
Abstracts of Australasian PhD Theses
Information
Bulletin of the Australian Mathematical Society , Volume 104 , Issue 1 , August 2021 , pp. 162 - 163
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

Footnotes

Thesis submitted to the Australian National University in April 2019; degree approved on 4 February 2020; supervisors Pierre Portal and Adam Sikora.

References

Axelsson, A., Keith, S. and McIntosh, A., ‘The Kato square root problem for mixed boundary value problems’, J. Lond. Math. Soc. (2) 74 (2006), 113–130.CrossRefGoogle Scholar
Axelsson, A., Keith, S. and McIntosh, A., ‘Quadratic estimates and functional calculi of perturbed Dirac operators’, Invent. Math. 163 (2006), 455–497.CrossRefGoogle Scholar
Bailey, J., ‘A Hardy–Littlewood maximal operator adapted to the harmonic oscillator’, Rev. Un. Mat. Argentina 59(2) (2018), 339–373.CrossRefGoogle Scholar
Bailey, J., ‘The Kato square root problem for divergence form operators with potential’, J. Fourier Anal. Appl. 26 (2020), Article ID 46, 58 pages.CrossRefGoogle Scholar
Maas, J., van Neerven, J. and Portal, P., ‘Whitney coverings and the tent spaces ${T}^{1,q}\left(\gamma \right)$ for the Gaussian measure’, Ark. Mat. 50 (2012), 379–395.CrossRefGoogle Scholar