Balinsky, Alexander; Ryan, John

Some sharp \(L^2\) inequalities for Dirac type operators. (English) Zbl 1141.15026

The stereographic projection corresponds to the Cayley transformation from \(S^{n}\mathbb N\) to the Euclidean space \(\mathbb{R}^{n}\), where \(N\) denotes the nord pole. The authors use this Cayley transformation to obtain some sharp \(L^2\) inequalities on the sphere for a family of Dirac type operators. The main tool is to employ a lowest eigenvalue for these operators and then use intertwining operators for the Dirac type operators to obtain analogous sharp inequalities in \(\mathbb{R}^{n}\).


15A66 Clifford algebras, spinors
26D10 Inequalities involving derivatives and differential and integral operators
34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
15A45 Miscellaneous inequalities involving matrices
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