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Limiting reiteration for real interpolation with slowly varying functions

✍ Scribed by Amiran Gogatishvili; Bohumír Opic; Walter Trebels

Publisher: John Wiley and Sons
Year: 2005
Tongue: English
Weight: 287 KB
Volume: 278
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200310228

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✦ Synopsis

Abstract

We 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)

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## Abstract This paper proposes an interpolation method called the “window function method” in which the sampling theorem and the window functions are combined. The cause of the generation of the interpolation error is the folding distortion due to the multiplication of the time‐limited window to t