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Reiteration for and exact relations between some real interpolation spaces. (English) Zbl 0776.46032

Function spaces, Proc. 2nd Int. Conf., Poznań/Pol. 1989, Teubner-Texte Math. 120, 238-247 (1991).
Summary: [For the entire collection see Zbl 0731.00012.]
For the real interpolation spaces \((A_ 0,A_ 1)_{f,q}\) with a parameter function \(f\) we prove a general reiteration result, where we need not assume some separation condition between the corresponding parameter functions. As one application we obtain a sharp embedding result between the spaces \((A_ 0,A_ 1)_{(\theta,b),q}\) obtained by using the function parameter \(f(t)=t^ \theta (1+|\log t|)^ b\). This result may be regarded as a generalization of some well-known embeddings between Lorentz-Zygmund spaces.

MSC:

46M35 Abstract interpolation of topological vector spaces

Citations:

Zbl 0731.00012
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