Interpolation of bilinear operators between quasi-Banach spaces
type: Item
instance of: scholarly article
title: Interpolation of bilinear operators between quasi-Banach spaces
zbMATH Open document ID: 1121.46018
author: Loukas Grafakos
author: Mieczysław Mastyło
published in: Positivity
publication date: 2006-11-03T00:00:00Z
review text: The authors study interpolation, generated by the abstract method of means, of bilinear operators between quasi-Banach spaces. They introduce a notion of special type of convexity for bilinear operators between quasi-Banach couples and prove a bilinear interpolation theorem using the methods of means, under the condition that the associated convolution operator is bounded on the parameter spaces involved in the construction of these methods. The convexity parameters of the bilinear operators that take values in the so-called natural quasi-Banach spaces are nicely determined by the types of the domains of the quasi-Banach spaces. The authors then give applications of these results in the context of interpolation between quasi-Banach spaces generated by the real method of interpolation as well as to Calderón--Lozanovski spaces that include, in particular, Orlicz spaces. Finally, they discuss the abstract \(K\)- or \(J\)-interpolation method for bilinear operators between quasi-Banach spaces satisfying weaker convexity type conditions, in particular, bilinear interpolation theorems for Lorentz--Zygmund spaces.
reviewed by: Carsten Michels
Mathematics Subject Classification ID: 46B70
Mathematics Subject Classification ID: 46M35
zbMATH DE Number: 5070790
zbMATH Keywords: interpolation
zbMATH Keywords: quasi-Banach spaces
zbMATH Keywords: multilinear interpolation
zbMATH Keywords: bilinear operators
zbMATH Keywords: Calderón-Lozanovski spaces
zbMATH Keywords: Lorentz-Zygmund spaces
MaRDI profile type: Publication
full work available at URL: s11117-005-0034-x
OpenAlex ID: W2070773288
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DOI: 10.1007/S11117-005-0034-X
description: scientific article; zbMATH DE number 5070790