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


  • Let C n Omega Subset mathbb {C}^{n} be a domain with smooth boundary, whose Bergman projection B B maps the Sobolev space H k 1 ( ) H^{k_{1}}(Omega ) (continuously) into H k 2 ( ) H^{k_{2}}(Omega ) . We establish two smoothing results: (i) the full Sobolev norm B f k 2 |Bf|_{k_{2}} is controlled by L 2 L^2 derivatives of f f taken along a single, distinguished direction (of order k 1 leq k_{1} ), and (ii) the projection of a conjugate holomorphic function in L 2 ( ) L^{2}(Omega ) is automatically in H k


published proceedings

  • Transactions of the American Mathematical Society

author list (cited authors)

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

citation count

  • 8

complete list of authors

  • Herbig, A-K||McNeal, J||Straube, E

publication date

  • July 2013