Duality of holomorphic function spaces and smoothing properties of the Bergman projection Academic Article uri icon

abstract

  • Let Ω {double subset} ℂn be a domain with smooth boundary, whose Bergman projection B maps the Sobolev space Hk1(Ω) (continuously) into Hk2 (Ω). We establish two smoothing results: (i) the full Sobolev norm ||Bf||k2 is controlled by L2 derivatives of f taken along a single, distinguished direction (of order ≤ k1), and (ii) the projection of a conjugate holomorphic function in L2(Ω) is automatically in Hk2 (Ω). There are obvious corollaries for when B is globally regular. © 2013 American Mathematical Society.

author list (cited authors)

  • Herbig, A., McNeal, J. D., & Straube, E. J.

citation count

  • 8

publication date

  • July 2013