Evans, W. D.; Opic, Bohumír; Pick, Luboš Real interpolation with logarithmic functors. (English) Zbl 1041.46011 J. Inequal. Appl. 7, No. 2, 187-269 (2002). The interpolation spaces in question consist of the vectors \(f\in X_0 +X_1\) satisfying \[ \Biggl(\int_0 ^\infty (t^{-\theta} \phi (t) K(x,\,y;\,X_0,\,X_1))^q t^{-1} \,dt \Biggr)^{1/q}<\infty \] (with the usual modification if \(q=\infty\)); here \(K(\dots)\) is the \(K\)-functional, and \(\phi\) is a function that behaves like some power of \(| \log t| \) near \(0\) and like some other power of \(\log t\) near \(\infty\). (In another version, a double logarithm is also incorporated in the definition of \(\phi\).) The emphasis is on Hardy-type inequalities, analogs of the Holmstedt formula, and reiteration theorems. Reviewer: S. V. Kislyakov (St. Petersburg) Cited in 51 Documents MSC: 46B70 Interpolation between normed linear spaces 47B38 Linear operators on function spaces (general) 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 47G10 Integral operators 26D10 Inequalities involving derivatives and differential and integral operators Keywords:\(K\)-functional; Hardy inequality; Holmstedt formula; reiteration theorem PDFBibTeX XMLCite \textit{W. D. Evans} et al., J. Inequal. Appl. 7, No. 2, 187--269 (2002; Zbl 1041.46011) Full Text: DOI