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special hermite expansion

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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A Hardy–Sobolev inequality for the twisted Laplacian
Part of
- Partial differential equations
Adimurthi, P. K. Ratnakumar, Vijay Kumar Sohani
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 147 / Issue 1 / February 2017

Published online by Cambridge University Press:

11 January 2017, pp. 1-23

Print publication:

February 2017
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We prove a strong optimal Hardy–Sobolev inequality for the twisted Laplacian on ℂn . The twisted Laplacian is the magnetic Laplacian for a system of n particles in the plane, corresponding to the constant magnetic field. The inequality we obtain is strong optimal in the sense that the weight cannot be improved. We also show that our result extends to a one-parameter family of weighted Sobolev spaces.