Holomorphic reproducing kernels in Reinhardt domains Academic Article uri icon

abstract

  • The orthogonal projection P0: L2() L2() {n-ary intersection} {holomorphic functions} (the Bergman projection) is studied, together with its analogue Ps: Ws() Ws() {n-ary intersection} {holomorphic functions}, for smooth bounded pseudoconvex complete Reinhardt domains Cn. It is shown that Ps maps the Sobolev space W() boundedly into itself for each r s. Explicit formulas are computed for the representing kernel functions for the case of the ball. 1984 by Pacific Journal of Mathematics.
  • The orthogonal projection P0: L2(Ω) → L2(Ω) {n-ary intersection} {holomorphic functions} (the Bergman projection) is studied, together with its analogue Ps: Ws(Ω) → Ws(Ω) {n-ary intersection} {holomorphic functions}, for smooth bounded pseudoconvex complete Reinhardt domains Ω ⊂ Cn. It is shown that Ps maps the Sobolev space W’(Ω) boundedly into itself for each r ≥ s. Explicit formulas are computed for the representing kernel functions for the case of the ball. © 1984 by Pacific Journal of Mathematics.

published proceedings

  • Pacific Journal of Mathematics

author list (cited authors)

  • Boas, H.

citation count

  • 10

complete list of authors

  • Boas, Harold

publication date

  • June 1984