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

Straube, Emil J.

doi:10.1090/S0002-9947-1989-0943308-3

Interpolation between Sobolev and between Lipschitz spaces of analytic functions on starshaped domains
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by Emil J. Straube PDF

Trans. Amer. Math. Soc. 316 (1989), 653-671 Request permission

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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