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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

Hardy inequalities for a magnetic Grushin operator with Aharonov-Bohm type magnetic field


Authors: L. Aermark and A. Laptev
Translated by: the authors
Original publication: Algebra i Analiz, tom 23 (2011), nomer 2.
Journal: St. Petersburg Math. J. 23 (2012), 203-208
MSC (2010): Primary 35P15; Secondary 81Q10
Published electronically: January 23, 2012
MathSciNet review: 2841670
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Abstract: A version of the Aharonov-Bohm magnetic field for a Grushin sub-elliptic operator is introduced; then its quadratic form is shown to satisfy an improved Hardy inequality.


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Additional Information

L. Aermark
Affiliation: Stockholm University, SE-106 91 Stockholm, Sweden
Email: lior@math.su.se

A. Laptev
Affiliation: Imperial College London, 180 Queen’s Gate, London SW7 2AZ, United Kingdom
Email: a.laptev@imperial.ac.uk

DOI: http://dx.doi.org/10.1090/S1061-0022-2012-01193-3
PII: S 1061-0022(2012)01193-3
Keywords: Hardy inequalities
Received by editor(s): November 28, 2010
Published electronically: January 23, 2012
Dedicated: Dedicated to the memory of M. Sh. Birman whose enormous scientific achievements continue to guide many generations of mathematicians. The strong school in Spectral Theory that he developed is renowned all over the world. All his pupils and colleagues remember Professor Birman as a wonderful person who was always ready to help. His warm and generous support certainly aided the second author of this paper to survive as a mathematician.
Article copyright: © Copyright 2012 American Mathematical Society