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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Interpolation between Sobolev and between Lipschitz spaces of analytic functions on starshaped domains


Author: Emil J. Straube
Journal: Trans. Amer. Math. Soc. 316 (1989), 653-671
MSC: Primary 46E15; Secondary 32A07, 46E35, 46M35
MathSciNet review: 943308
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Abstract: We show that on a starshaped domain $ \Omega $ in $ {\operatorname{C} ^n}$ (actually on a somewhat larger, biholomorphically invariant class) the $ {\mathcal{L}^p}$-Sobolev spaces of analytic functions form an interpolation scale for both the real and complex methods, for each $ p,\;0 < p \leqslant \infty $. The case $ p = \infty $ gives the Lipschitz scale; here the functor $ {(,)^{[\theta ]}}$ has to be considered (rather than $ {(,)_{[\theta ]}}$).


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1989-0943308-3
PII: S 0002-9947(1989)0943308-3
Keywords: Complex interpolation, real interpolation, Sobolev spaces of analytic functions, Lipschitz spaces of analytic functions, starshaped domains
Article copyright: © Copyright 1989 American Mathematical Society