Title: Singularity and Regularity --- Local and Global

There exists a smoothly bounded, pseudoconvex domain in $\complex^2$ for which the Bergman projection fails to preserve the class of functions which are globally smooth up to the boundary. The counterexample is explained and placed in a wider context through a broader discussion of the local and global regularity of solutions to subelliptic and more degenerate partial differential equations in various function spaces.

1991 Mathematics Subject Classification: 32F20, 35N15, 35P30, 42B99

Keywords and Phrases: Hypoellipticity, global regularity, Bergman projection, $\bar\partial$--Neumann problem.

Full text: dvi.gz 24 k, dvi 52 k, ps.gz 78 k.

Home Page of DOCUMENTA MATHEMATICA