Nilsson, Per; Peetre, Jaak On the K functional between \(L^ 1\) and \(L^ 2\) and some other K functionals. (English) Zbl 0617.46077 J. Approximation Theory 48, 322-327 (1986). 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.) Cited in 2 ReviewsCited in 4 Documents 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 PDF BibTeX XML Cite \textit{P. Nilsson} and \textit{J. Peetre}, J. Approx. Theory 48, 322--327 (1986; Zbl 0617.46077) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.