Abstract
We conclude the book by applying some of the results of earlier chapters to certain approximation problems in LP-norm for analytic and harmonic functions. By duality these problems can be reformulated as “stability problems” in Sobolev spaces, which can be given complete solutions in terms of capacities. The main results depend on Theorem 9.1.3 (or Theorem 10.1.1), but mostly only on the easy case when the space is W1, P. The more complicated case of spaces involving higher derivatives is used only in the last section, Section 11.5, but even this section can very well be read before studying the proof of the theorem.
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© 1996 Springer-Verlag Berlin Heidelberg
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Adams, D.R., Hedberg, L.I. (1996). Rational and Harmonic Approximation. In: Function Spaces and Potential Theory. Grundlehren der mathematischen Wissenschaften, vol 314. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03282-4_11
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DOI: https://doi.org/10.1007/978-3-662-03282-4_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08172-9
Online ISBN: 978-3-662-03282-4
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