Cwikel, Michael; Nilsson, Per Interpolation of Marcinkiewicz spaces. (English) Zbl 0551.46052 Math. Scand. 56, 29-42 (1985). For each non-negative concave function \(\phi\) (t), the Marcinkiewicz space \(M_{\phi}\) consists of all measurable functions f such that \((\phi (t))^{-1}\int^{t}_{0}f^*(s)ds\leq C\) for all \(t>0\) and some constant C. Interpolation spaces with respect to couples \((M_{\phi_ 0},M_{\phi_ 1})\) of such spaces are considered. It is shown that for certain choices of \(\phi_ 0\) and \(\phi_ 1\) these interpolation spaces can be characterized by a monotonicity property with respect to the K- functional, that is \((M_{\phi_ 0},M_{\phi_ 1})\) is a Caldéron couple. Cited in 5 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.) Keywords:Marcinkiewicz space; interpolation spaces; K-functional; Calderón couple PDFBibTeX XMLCite \textit{M. Cwikel} and \textit{P. Nilsson}, Math. Scand. 56, 29--42 (1985; Zbl 0551.46052) Full Text: DOI EuDML