THE BEURLING AND CAUCHY TRANSFORM WITH NEW SPACES

Abstract

Let X be a compact plane set. Then R(X) is the uniform algebra of all continuous functions on X which may be uniformly approximated on X by rational functions with poles off X. Some results which contain the Beuring and Cauchy transforms are true for R(X). Our aim in this paper is to change the uniform algebra R(X) with some other new uniform algebras, especially A(X) which is the uniform algebra of all holomorphic functions on the interior of X.