Limiting reiteration for real interpolation with slowly varying functions
Copyright policy )Limiting reiteration for real interpolation with slowly varying functions
AbstractWe present reiteration formulae with limiting values θ = 0 and θ = 1 for a real interpolation method involving slowly varying functions. Applications to the Lorentz–Karamata spaces, the Fourier transform and the Riesz potential are given. In particular, our results yield improvements of limiting Sobolev‐type embeddings due to Trudinger, Hansson, Brézis and Wainger, Edmunds, Gurka and Opic, Fusco, Lions and Sbordone, et al., and they are related to those of Edmunds, Kerman and Pick, or Pustylnik. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
- Czech Academy of Sciences Czech Republic
- Academy of Sciences Library Czech Republic
- TU Darmstadt Germany
slowly varying functions, weighted inequalities, limiting Sobolev-type embeddings, Interpolation between normed linear spaces, \(K\)-functional, limiting reiteration, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), real interpolation, Linear operators on function spaces (general), Lorentz-Karamata spaces, Fourier transform, Riesz potential, Inequalities for sums, series and integrals, Rate of growth of functions, orders of infinity, slowly varying functions, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, K-functional
slowly varying functions, weighted inequalities, limiting Sobolev-type embeddings, Interpolation between normed linear spaces, \(K\)-functional, limiting reiteration, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), real interpolation, Linear operators on function spaces (general), Lorentz-Karamata spaces, Fourier transform, Riesz potential, Inequalities for sums, series and integrals, Rate of growth of functions, orders of infinity, slowly varying functions, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, K-functional
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