Bounded mean oscillation on the bidisk and the operator BMO
type: Item
instance of: scholarly article
title: Bounded mean oscillation on the bidisk and the operator BMO
zbMATH Open document ID: 1010.47017
author: Sandra Pott
author: Cora Sadosky
published in: Journal of Functional Analysis
publication date: 2002-09-08T00:00:00Z
review text: The authors study the BMO spaces in two variables as operator valued BMO functions in one variable and give strict inclusions in the BMO scale. In particular, it is shown that there exists a symbol \(b\) defined on the bidisk such that the little Hankel operator \(\gamma_b=P^\bot_1 P_2^\bot b P_2^\bot P_1^\bot\) is bounded on the set of all products of normalized Szegö kernels \(\{k_{z_1}\otimes{k_{z_2}}: z_1, z_2 \in D\}\) but does not extend to a bounded linear operator on \(H^2 (T^2)\).
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 47A56
zbMATH DE Number: 1797577
zbMATH Keywords: BMO spaces
zbMATH Keywords: Hankel operators
reviewed by: N. Karapetiants
MaRDI profile type: Publication
full work available at URL: jfan.2001.3822
OpenAlex ID: W1990060587
cites work: Q4865548
cites work: Q4188518
cites work: Boundedness of Hankel Matrices
cites work: Some remarks on Banach spaces in which martingale difference sequences are unconditional
cites work: Carleson measure on the bi-disc
cites work: Some recent developments in Fourier analysis and 𝐻^{𝑝}-theory on product domains
cites work: Factorization theorems for Hardy spaces in several variables
cites work: Nehari and Nevanlinna-Pick problems and holomorphic extensions in the polydisk in terms of restricted BMO
cites work: Characterizations of bounded mean oscillation
cites work: Bounded mean oscillation on the polydisk
cites work: Characterizations of bounded mean oscillation on the polydisk in terms of Hankel operators and Carleson measures
cites work: LOGARITHMIC GROWTH FOR MATRIX MARTINGALE TRANSFORMS
cites work: Q5314026
cites work: A transference approach to estimates of vectorial Hankel operators
cites work: Matrix valued paraproducts
cites work: Counterexample to the infinite dimensional carleson embedding theorem
cites work: Q3713006
cites work: Dyadic shifts and a logarithmic estimate for Hankel operators with matrix symbol
cites work: Sharp estimates in vector Carleson imbedding theorem and for vector paraproducts
DOI: 10.1006/JFAN.2001.3822
description: scientific article; zbMATH DE number 1797577