Hausdorff content and rational approximation in fractional Lipschitz norms

O’Farrell, Anthony G.

doi:10.1090/S0002-9947-1977-0432887-2

Hausdorff content and rational approximation in fractional Lipschitz norms
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by Anthony G. O’Farrell PDF

Trans. Amer. Math. Soc. 228 (1977), 187-206 Request permission

Abstract:

For $0 < \alpha < 1$, we characterise those compact sets X in the plane with the property that each function in the class ${\text {lip}}(\alpha ,X)$ that is analytic at all interior points of X is the limit in ${\text {Lip}}(\alpha ,X)$ norm of a sequence of rational functions. The characterisation is in terms of Hausdorff content.

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