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Global analyticity for $$\square_ b$$ on three dimensional pseudoconvex CR manifolds. (English) Zbl 0791.35087
The authors study global real analytic regularity for the canonical solution to the equation $$\overline {\partial}_ b u=f$$ on a compact, real analytic, three (real) dimensional pseudoconvex CR manifold $$M$$. The hypotheses imposed are these:
1) $$u$$ is in the range of $$\overline {\partial}_ b^*$$, which is always the case if $$\overline {\partial}_ b$$ has closed range;
2) there exists a globally defined purely imaginary real analytic vector field $$T$$, complementary to $$T^{1,0}+ T^{0,1}$$, such that if $$L$$ is any smooth section of $$T^{1,0}$$ then $$[T,L]$$ is a section of $$T^{1,0}+ \overline {T^{1,0}}$$.
Both of these conditions are known to hold when $$M$$ is the boundary of a strongly pseudoconvex domain in space, or when $$M$$ is the boundary of a Reinhardt domain.

##### MSC:
 35N15 $$\overline\partial$$-Neumann problems and formal complexes in context of PDEs 32W05 $$\overline\partial$$ and $$\overline\partial$$-Neumann operators 32T99 Pseudoconvex domains
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