Compatibility operators for degenerated elliptic equations on the ball and Heisenberg group
Differential operators on the Heisenberg group and odd dimensional spheres are derived whose smooth solutions are exactly the boundary values of smooth solutions of certain degenerate elliptic operators generalizing the Laplace-Beltrami operator in the Bergman metric on the Siegel domain or the complex ball. On the Heisenberg group these ''compatibility operators'' are products of Folland-Stein \({\mathcal L}_{\alpha}\) operators. A transformation law for these operators under the Cayley transform is derived as well as explicit formulae for their fundamental solutions.
elliptic operators generalizing the Laplace-Beltrami operator in the Bergman metric on the Siegel domain
scientific article; zbMATH DE number 3855821