A decomposition theorem for BMO and applications
type: Item
instance of: scholarly article
title: A decomposition theorem for BMO and applications
zbMATH Open document ID: 0593.47027
DOI: 10.1016/0022-1236(86)90038-8
author: Stephen Semmes
author: Richard Rochberg
published in: Journal of Functional Analysis
publication date: 1986-01-01T00:00:00Z
review text: A result of Coifman and Rochberg allows one to decompose an analytic function in the upper half-plane lying in certain function spaces as a sum of coefficients times normalized rational functions, and they showed how to obtain Peller's characterization of trace class Hankel operators from this. The paper under review strengthens the above decomposition theorem by obtaining pointwise estimates on the coefficients. This is used to give pointwise estimates for the singular values of a Hankel operator, the first Calderon commutator, and a product of two Hankel operators, Hankel operators a (converse) estimate that is close to pointwise is given for the derivative of the (Poisson extension of the) symbol in terms of the singular values. A key point is to estimate the singular values of a sum of rank one operators. If the vectors involved are orthonormal this is trivial, but that never happens in real life. The authors introduce a condition (''nearly weakly orthonormal'') that does arise in examples and is good enough to give the right kind of estimates.
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 46E15
zbMATH DE Number: 3953624
zbMATH Keywords: commutators
zbMATH Keywords: BMO
zbMATH Keywords: Peller's characterization of trace class Hankel operators
zbMATH Keywords: decomposition theorem
zbMATH Keywords: pointwise estimates
zbMATH Keywords: singular values of a Hankel operator
zbMATH Keywords: first Calderon commutator
zbMATH Keywords: singular values of a sum of rank one operators
zbMATH Keywords: nearly weakly orthonormal
MaRDI profile type: Publication
full work available at URL: 0022-1236(86)90038-8
OpenAlex ID: W2062977557
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description: scientific article; zbMATH DE number 3953624