ABSTRACT
As mentioned in Chapter 18, there does not exist a solution to the equation ∂ ¯ M × M K = [ Δ ] https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315140445/fbe50be4-2923-45ad-961d-51ed68ffe025/content/in2123.tif"/> , except for very specialized M. However, in this chapter, we shall construct a solution to the equation ∂ ¯ M × M K = [ Δ ] https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315140445/fbe50be4-2923-45ad-961d-51ed68ffe025/content/in2124.tif"/> for a strictly convex Af, modulo a kernel which as an operator acts nontrivially only on forms of bottom and top degree. We shall then abuse the notation and call K a fundamental solution for the tangential Cauchy–Riemann complex. We present two fundamental solutions for the tangential Cauchy–Riemann complex. The second solution will be derived from the first and it will play a key role in the local solution to the tangential Cauchy–Riemann equations in the same way that the Bochner-Martinelli kernel plays a role in the local solution to the Cauchy–Riemann equations.
