Fundamental Solutions on the Heisenberg Group
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2019
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This paper is an expository note mainly concentrated on section 2,4,5,6 and 7 of Folland and Stein's work. We first review some definitions and properties of CR manifolds,∂ ̅_b complex and Heisenberg groups. We then derive the explicit form of the Laplacian □_b and deduce the problem of □_b to the operator L_α. The major part of the paper is to find the fundamental solutions for L_α on the Heisenberg group and to compute the constant c_α. Last we analyze the solutions of L_α f=g to finish the paper.
This paper is an expository note mainly concentrated on section 2,4,5,6 and 7 of Folland and Stein's work. We first review some definitions and properties of CR manifolds,∂ ̅_b complex and Heisenberg groups. We then derive the explicit form of the Laplacian □_b and deduce the problem of □_b to the operator L_α. The major part of the paper is to find the fundamental solutions for L_α on the Heisenberg group and to compute the constant c_α. Last we analyze the solutions of L_α f=g to finish the paper.
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CR manifold, Heisenberg group, fundamental solution, CR manifold, Heisenberg group, fundamental solution