UC Irvine

The Dunford-Pettis property is shown to hold for the uniform algebra A(Ω) and its dual for some standard domains Ω, including strongly pseudoconvex bounded domains in Cn, pseudoconvex bounded domains of finite type in C2, and bounded domains in C. Previously the result was known for the unit ball and unit polydisc in Cn. Techniques used involve Bourgain algebras, Hankel operators, properties of the Bergman kernel, quasi-metrics on the boundary, and theory. © 1994 The London Mathematical Society.