A unified theory of commutator estimates for a class of interpolation methods
type: Item
instance of: scholarly article
title: A unified theory of commutator estimates for a class of interpolation methods
zbMATH Open document ID: 1022.46017
author: Michael Cwikel
author: N. J. Kalton
author: Richard Rochberg
author: Mario Milman
published in: Advances in Mathematics
publication date: 2002-11-28T00:00:00Z
review text: In this interesting paper, a general family of interpolation methods is introduced which includes, as special cases, the real and complex methods and also the so-called \(\pm\) method defined by Peetre. Derivation operators \(\Omega\) and translation operators \(\mathcal R\) are introduced for all methods of this family. A theorem is proved about the boundedness of the commutators \([T,\Omega]\) and \([T, \mathcal R]\) for operators \(T\) which are bounded on the spaces of the pair to which the interpolation method is applied. This extends and unifies results previously known for derivation and translation operators in the contexts of real and complex methods.
reviewed by: Nicolae Popa
Mathematics Subject Classification ID: 46B70
Mathematics Subject Classification ID: 46H35
zbMATH DE Number: 1836808
zbMATH Keywords: derivation operator
zbMATH Keywords: commutator estimate
zbMATH Keywords: pseudolattice
zbMATH Keywords: real interpolation
zbMATH Keywords: complex interpolation
zbMATH Keywords: plus-minus interpolation method
zbMATH Keywords: Lions-Schechter interpolation space
MaRDI profile type: Publication
full work available at URL: aima.2001.2061
OpenAlex ID: W1976992261
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A unified theory of commutator estimates for a class of interpolation methods (DOI)
DOI: 10.1006/AIMA.2001.2061