Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

BMO rational approximation and one-dimensional Hausdorff content
HTML articles powered by AMS MathViewer

by Joan Verdera PDF
Trans. Amer. Math. Soc. 297 (1986), 283-304 Request permission

Abstract:

Let $X \subset {\mathbf {C}}$ be compact and let $f \in \operatorname {VMO} ({\mathbf {C}})$. We give necessary and sufficient conditions on $f$ and $X$ for ${f_{|X}}$ to be the limit of a sequence of rational functions without poles on $X$ in the norm of $\operatorname {BMO} (X)$, the space of functions of bounded mean oscillation on $X$. We also characterize those compact $X \subset {\mathbf {C}}$ with the property that the restriction to $X$ of each function in $\operatorname {VMO} ({\mathbf {C}})$, which is holomorphic on $\mathring {X}$, is the limit of a sequence of rational functions with poles off $X$. Our conditions involve the notion of one-dimensional Hausdorff content. As an application, a result related to the inner boundary conjecture is proven.
References
Similar Articles
Additional Information
  • © Copyright 1986 American Mathematical Society
  • 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