zbMATH — the first resource for mathematics

Homotopy formulas in the tangential Cauchy-Riemann complex. (English) Zbl 0707.35105
Mem. Am. Math. Soc. 434, 121 p. (1990).
Conjugation of the classical kernels of Bochner-Martinelli and Koppelman- Leray with the FBI minitransform - a simplified version of the Fourier- Bros-Iagolnitzer transform - is used to construct homotopy operators in the tangential Cauchy-Riemann complex. On a real hypersurface in complex space the presence of supporting manifolds is exploited to modify the phase function and ensure the positivity of its imaginary part.
Reviewer: J.Marschall

MSC:
 35N15 $$\overline\partial$$-Neumann problems and formal complexes in context of PDEs 58J10 Differential complexes
Full Text: