BMO rational approximation and one-dimensional Hausdorff content

Author:
Joan Verdera

Journal:
Trans. Amer. Math. Soc. **297** (1986), 283-304

MSC:
Primary 30E10; Secondary 28A20, 30B40, 46E15

DOI:
https://doi.org/10.1090/S0002-9947-1986-0849480-5

MathSciNet review:
849480

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be compact and let . We give necessary and sufficient conditions on and for to be the limit of a sequence of rational functions without poles on in the norm of , the space of functions of bounded mean oscillation on . We also characterize those compact with the property that the restriction to of each function in , which is holomorphic on , is the limit of a sequence of rational functions with poles off . Our conditions involve the notion of one-dimensional Hausdorff content. As an application, a result related to the inner boundary conjecture is proven.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1986-0849480-5

Keywords:
Rational function,
approximation,
BMO,
Hausdorff content

Article copyright:
© Copyright 1986
American Mathematical Society