Exact descriptions of some \(K\) and \(E\) functionals
If \(f^*\) is the rearrangement function of \(f\), then one has for Peetre's \(K\)-functional \[ K(t, f,L_1,L_\infty)= \int^t_0 f^*(s)ds \] for the interpolation couple \(\{L_1,L_\infty\}\). It is the main aim of the paper to calculate \(K(t, f,L_{p,q}, L_\infty)\), more general \(K(t, f, X,L_\infty)\), where \(X\) is a quasi-normed function lattice, and \(K(t, f,L_{p/q,1}, L_{p,q})\).
scientific article; zbMATH DE number 1042514
scientific article