Remarks on Global Irregularity in the ∂̄–Neumann Problem
نویسنده
چکیده
The Bergman projection on a general bounded, smooth pseudoconvex domain in two complex variables need not be globally regular, that is, need not preserve the class of all functions that are smooth up to the boundary. In this article the construction of the worm domains is reviewed, with emphasis on those features relevant to their role as counterexamples to global regularity. Prior results, and related issues such as the commutation method and compactness estimates, are discussed. A model in two real variables for global irregularity is discussed in detail. Related work on real analytic regularity, both local and global, is summarized. Several open questions are posed.
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