Orthogonal projections onto subspaces of the harmonic Bergman space Academic Article uri icon

abstract

  • Let Ω ⊂ Rm be a bounded, smooth domain. We construct a continuous linear operator T: W0(Ω) → W0(Ω) which for all k ∈ (N {n-ary union} {∞}) is actually continuous from Wk(Ω) → W0k(Ω), and which moreover has the property that ST = S, for any orthogonal projection S of W0(ω) onto a subspace of the harmonic Bergman space. That is, the operator assigns to each function a function vanishing to high (infinite if k = ∞) order at bΩ, but with the same projection. S can in particular be the harmonic Bergman projection, or, when Ω ⊂ Cn, the (analytic) Bergman projection. The question whether such an operator exists arises for example in connection with regularity properties of the Bergman projection and their intimate connection with boundary regularity of holomorphic mappings. © 1986 by Pacific Journal of Mathematics.

author list (cited authors)

  • Straube, E.

citation count

  • 2

publication date

  • June 1986