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
Full-text PDF Free Access
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