Closure properties of families of Cauchy-Stieltjes transforms

Authors:
R. A. Hibschweiler and T. H. MacGregor

Journal:
Proc. Amer. Math. Soc. **105** (1989), 615-621

MSC:
Primary 30E20

DOI:
https://doi.org/10.1090/S0002-9939-1989-0938912-8

MathSciNet review:
938912

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Abstract: For let denote the class of functions defined for by integrating against a complex measure on . The main results in this paper assert that is closed under multiplication by a function holomorphic for and under composition with a function holomorphic and satisfying for when . The last result is shown to be false when .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1989-0938912-8

Keywords:
Holomorphic function,
Cauchy-Stieltjes transforms,
complex measures

Article copyright:
© Copyright 1989
American Mathematical Society