Commutator and other second order estimates in real interpolation theory
type: Item
instance of: scholarly article
title: Commutator and other second order estimates in real interpolation theory
zbMATH Open document ID: 0655.41005
DOI: 10.1007/BF02384398
author: Richard Rochberg
author: G. Weiss
author: Björn D. Jawerth
published in: Arkiv för Matematik
publication date: 1986-01-01T00:00:00Z
review text: Etant donné \((\bar A=(A_ 0,A_ 1)\) un couple d'espaces de Banach, et la fonction K qui intervient dans la théorie de l'interpolation: \(\forall a\in A_ 0,A_ 1\), \(\forall t>0\), \(K(t,a,\bar A)=_{a=a_ 0+a_ 1}(Max(\| a_ 0\|_{A_ 0},t\| a_ 1\|_{A_ 1}))\), les auteurs introduisent une application de ``meilleure approximation'': \(t\to D(r| a=D_ k(r,\bar A| a=a_ 0(r)\) avec soit \(c>1\) \(k(r,a)\leq Max(\| a_ 0(r)\|_ 1,t\| a_ 1(t)\|_ 1\leq ck(r,a)\) \(\forall t\), ainsi que l'opérateur \(\Omega(a):\) \(\Omega(a)=\int^{\infty}_{0}(D_ k(r)- I\chi_{(1\infty)})a dt/t\). Si T est un opérateur linéaire de \(A_ 0+A_ 1\to B_ 0+B_ 1\) (continue de Ai dans Bi, \(i=1,2)\) alors: \([T,\Omega]=T\Omega -\Omega T:a\to [T,\Omega](a)=\int^{\infty}_{0}[T,D(r)]a dt/t\), où \([T,D(r)](a)=(TD(r),\bar A)-D(r,\bar B)T)(a)\), est linéaire continue de \(\bar A_{\theta q}\) dans \(\bar B_{\theta q}\). Ils étudient D et \(\Omega\) associés à d'autres fonctions que la fonction k, en particulier pour la fonction E, k donnent des exemples d'application ({\S} 4).
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 46M35
zbMATH DE Number: 4069487
zbMATH Keywords: commutator
zbMATH Keywords: second order estimates
reviewed by: Marie-Therese Lacroix
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4069487