On the Grushin operator and hyperbolic symmetry

Author:
William Beckner

Journal:
Proc. Amer. Math. Soc. **129** (2001), 1233-1246

MSC (2000):
Primary 58J70, 35A15

DOI:
https://doi.org/10.1090/S0002-9939-00-05630-6

Published electronically:
October 10, 2000

MathSciNet review:
1709740

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Abstract | References | Similar Articles | Additional Information

Complexity of geometric symmetry for differential operators with mixed homogeniety is examined here. Sharp Sobolev estimates are calculated for the Grushin operator in low dimensions using hyperbolic symmetry and conformal geometry.

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Additional Information

**William Beckner**

Affiliation:
Department of Mathematics, University of Texas at Austin, Austin, Texas 78712-1082

Email:
beckner@math.utexas.edu

DOI:
https://doi.org/10.1090/S0002-9939-00-05630-6

Received by editor(s):
March 19, 1999

Received by editor(s) in revised form:
July 2, 1999

Published electronically:
October 10, 2000

Additional Notes:
This work was partially supported by the National Science Foundation.

Communicated by:
Christopher D. Sogge

Article copyright:
© Copyright 2000
American Mathematical Society