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On the K functional between $$L^ 1$$ and $$L^ 2$$ and some other K functionals. (English) Zbl 0617.46077
An explicit formula for the K-functional between $$L^ 1$$ and $$L^ 2$$ is given. It was suggested by and contains as a special case the Valiron- Landau lemma in function theory [see P. Duren, Univalent functions (1983; Zbl 0514.30001), pp. 104-105]. (The preface contains also an anecdote about G. Freud, to whose memory the entire volume is devoted.)

##### MSC:
 46M35 Abstract interpolation of topological vector spaces 46E30 Spaces of measurable functions ($$L^p$$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 01A70 Biographies, obituaries, personalia, bibliographies
##### Keywords:
Orlicz space; K-functional; Valiron-Landau lemma
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##### References:
 [1] Bergh, J; Löfström, J, Interpolation spaces. an introduction, () · Zbl 0344.46071 [2] Duren, P.L, Univalent functions, () · Zbl 0398.30010 [3] Holmstedt, T, Interpolation of quasinormed spaces, Math. scand., 26, 177-199, (1970) · Zbl 0193.08801 [4] Landau, E, Über die blochsche konstante und zwei verwandte weltkonstanten, Math. Z., 30, 608-634, (1929) · JFM 55.0770.03 [5] Valiron, G, Sur le théorème de M. Bloch, Rend. circ. mat. Palermo, 54, 76-82, (1929) · JFM 56.0269.02
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