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Interpolation of Operators on Scales of Generalized Lorentz‐Zygmund Spaces
Author(s) -
Evans W. D.,
Opic B.,
Pick L.
Publication year - 1996
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19961820108
Subject(s) - mathematics , interpolation (computer graphics) , interpolation space , birkhoff interpolation , hardy space , intersection (aeronautics) , limiting , pure mathematics , lorentz transformation , mathematical analysis , linear interpolation , polynomial interpolation , functional analysis , computer science , frame (networking) , mechanical engineering , biochemistry , chemistry , physics , classical mechanics , polynomial , engineering , gene , aerospace engineering , telecommunications
We define generalized Lorentz‐Zygmund spaces and obtain interpolation theorems for quasilinear operators on such spaces, using weighted Hardy inequalities. In the limiting cases of interpolation, we discover certain scaling property of these spaces and use it to obtain fine interpolation theorems in which the source is a sum of spaces and the target is an intersection of spaces. This yields a considerable improvement of the known results which we demonstrate with examples. We prove sharpness of the interpolation theorems by showing that the constraints on parameters are necessary for the interpolation theorems.