The Quarterly Journal of Mathematics · 2010 · 33 citations · 0 references
Natural SciencesMathematicsAlgorithmsComputational GeometryTopologyHarmonic AnalysisInterpolation TechniquesInterpolation InequalitiesInterpolation SpacesInterpolation Theory
We present a real interpolation method defined with slowly varying functions and rearrangement invariant spaces as parameters. We prove generalized Holmstedt-type formulas for this method that are applied to obtain reiteration theorems, including the limiting cases θ = 0 and θ = 1. To describe the spaces arising from reiteration theorems in the limiting cases, new interpolation constructions are introduced. Among the techniques used, we establish new Hardy-type inequalities for rearrangement invariant spaces which have independent interest.