On boundary value problems for some conformally invariant differential operators
Journal article, 2016

We study boundary value problems for some differential operators on Euclidean space and the Heisenberg group which are invariant under the conformal group of a Euclidean subspace, respectively, Heisenberg subgroup. These operators are shown to be self-adjoint in certain Sobolev type spaces and the related boundary value problems are proven to have unique solutions in these spaces. We further find the corresponding Poisson transforms explicitly in terms of their integral kernels and show that they are isometric between Sobolev spaces and extend to bounded operators between certain L-p-spaces.The conformal invariance of the differential operators allows us to apply unitary representation theory of reductive Lie groups, in particular recently developed methods for restriction problems.

complementary series

fractional laplacian

Poisson transform

Plancherel formula

Boundary value problem

unitary

extension problem

Author

Genkai Zhang

University of Erlangen-Nuremberg (FAU)

B Orsted

Aarhus University

Genkai Zhang

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Communications in Partial Differential Equations

0360-5302 (ISSN) 1532-4133 (eISSN)

Vol. 41 4 609-643

Subject Categories

Mathematics

DOI

10.1080/03605302.2015.1123275

More information

Latest update

3/29/2018