DUALITY OF HOLOMORPHIC FUNCTION SPACES AND SMOOTHING PROPERTIES OF THE BERGMAN PROJECTION Academic Article uri icon

abstract

  • 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

    authors

published proceedings

  • TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY

author list (cited authors)

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

citation count

  • 8

complete list of authors

  • Herbig, A-K||McNeal, JD||Straube, EJ

publication date

  • February 2014