On rearrangements of vector-valued \(H_ 1\)-functions
type: Item
instance of: scholarly article
title: On rearrangements of vector-valued \(H_ 1\)-functions
zbMATH Open document ID: 0693.46045
DOI: 10.1007/BF02386121
published in: Arkiv för Matematik
publication date: 1988-01-01T00:00:00Z
review text: Let X be a Banach space, \(T={\mathbb{R}}/{\mathbb{Z}}\), \(L_ 1(T,X)\) be the space of all Bochner integrable functions on T and \(H^ a_ 1(X)\) be the space of all \(f\in L_ 1(T,X)\) such that \(f=\sum_{n}c_ na_ n\), where each \(a_ n\) is an atom and \(\sum | c_ n| <\infty\). The function \(f\in L_ 1(T,X)\) is called to be a rearrangement of \(g\in L_ 1(T,X)\) if \(\mu_ f=\mu_ g\) where \(\mu_ f\) is the Borel measure on X defined by \(\mu_ f(B)=\lambda (f^{-1}(B))\) (B\(\subset X\) and \(\lambda\) is a normalized Haar measure on T). It is found the necessary and sufficient conditions that \(f\in L_ 1(T,X)\) has a rearrangement in \(H^ a_ 1(X)\).
Mathematics Subject Classification ID: 46E40
Mathematics Subject Classification ID: 46J15
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 4134838
zbMATH Keywords: rearrangements of vector-valued functions
zbMATH Keywords: space of all Bochner integrable functions
zbMATH Keywords: normalized Haar measure
author: N. J. Kalton
reviewed by: Mart Abel
MaRDI profile type: Publication
cites work: Hardy Spaces of Vector-Valued Functions: Duality
cites work: Q4081768
cites work: Hardy Spaces and Rearrangements
cites work: On the integrability of the ergodic maximal function
cites work: Nonlinear commutators in interpolation theory
cites work: Calderón-Zygmund theory for operator-valued kernels
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description: scientific article; zbMATH DE number 4134838