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Commutators and interpolation methods

✍ Scribed by María J. Carro; Joan Cerdà; Javier Soria

Book ID
112781380
Publisher
Springer Netherlands
Year
1995
Tongue
English
Weight
642 KB
Volume
33
Category
Article
ISSN
0004-2080

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We study the relationship between Schechter's methods of complex interpolation and the so called commutator estimates. We obtain new commutator theorems and prove characterizations of the Domain and Range spaces associated with the corresponding quasilogarithmic operator. Our methods also provide a

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## Abstract The aim of this note is to show how all the commutator estimates of two recent papers, by M. Cwikel, N. Kalton, M. Milman, and R. Rochberg and by N. Krugljak and M. Milman, can be considered as special cases of the method of couples of interpolators introduced by M. J. Carro, J. Cerdà a

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A general family of interpolation methods is introduced which includes, as special cases, the real and complex methods and also the so-called AE or G 1 and G 2 methods defined by Peetre and Gustavsson-Peetre. Derivation operators O and translation operators R are introduced for all methods of this f