Abstract
Let Z denote the holomorphic tangential vector field to the generalized upper-half plane = {(z1,z) isin; ℂ2; Ρ = Im z 1 -|z|4 > 0}. In our terminology, t = Re z1. Consider the ?b operator on the boundary of , D,Ⅎ = -1/2(ZZ + ZZ); note that Ⅎ is nowhere elliptic, but it is subelliptic with step three. The principal result of this paper is the derivation of an explicit fundamental solution F to Ⅎ. Our approach is based on special functions and their properties.
Original language | English |
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Pages (from-to) | 407-433 |
Number of pages | 27 |
Journal | Analysis and Applications |
Volume | 16 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1 May 2018 |
Scopus Subject Areas
- Analysis
- Applied Mathematics
User-Defined Keywords
- fundamental solution
- special functions
- Subelliptic operator