By Jaak Peetre (auth.), Michael Cwikel, Jaak Peetre (eds.)

**Read or Download Interpolation Spaces and Allied Topics in Analysis: Proceedings of the Conference held in Lund, Sweden, August 29 – September 1, 1983 PDF**

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**Additional resources for Interpolation Spaces and Allied Topics in Analysis: Proceedings of the Conference held in Lund, Sweden, August 29 – September 1, 1983**

**Example text**

Property Let X be an order continuous on a ~-finite measure space Banach (~,z,~). lattice with the Fatou Then the following are equivalent: (i) There exists functions w0,wl, -~, a constant 4>0 such that for all choices v0,v I the couples couples with constant ~. (Xw0,Xwl) and (Xv0,×Vl) of weight are relative 56 ~i) There exists a constant choices of weight C>O such that for some @ C (0,I) and all functions w0,wl, v0,v I the spaces Xw~-~w ~ and Xv~_@v~ u are relative C-K spaces with respect (~i) For some measurable p E [i,~), X coincides, space of functions and subset ~, of ~, some weight up to equivalence f vanishing ]If [I p a to (Xw0,Xwl) ~ (Xv0,Xvl).

Itself (the s e m i d i r e c t is in f a c t For different different Vx fore natural Problem space with. study a group isometries), of the (O n t into spaces). = h(f0~) Vf functions, Hp on t h e form (see or of (for = G O In t h e with of a r e a r r a n g e m e n t either analytic starts isometry ideal, operators ~; space of t h e p o s i t i v e every remarks. invariant started V ( t n) of . isometrically (which h a s m a n y cases into itself. transformations question Hilbert acts V~ isometry ~ C~ some general function of G = Aut(U) Let and (Rf) (z) the reflection = f(z) be the z ~ reflection operator.

I In view of the work of Brudny~ [8, 16, 18]) an equivalent is that each normed interpolation ]l~denotes for~ulation (iii) and and Krugljak of such results space A with respect to the Banach couple A = (A0,AI) has an (equivalent) J]K~t,a;~) JJ~ wherell for the of Banach spaces A have been shown to have a property analogous Property in terms of the Ki-functional. Remarks spaces to their work has been a long series of pa- pers in which many different (A0,AI) [6] (independently) the interpolation norm of the simple some suitable form Ilal] A = lattice norm on a space of real valued functions on (0,~).