OPERATOR-VALUED DYADIC BMO SPACES

We consider BMO spaces of operator-valued functions, among them the space of operator-valued functions B which define a bounded paraproduct on L2(H). We obtain several equivalent formulations of ∥πB∥ in terms of the norm of the "sweep" function of B or of averages of the norms of martingal...

Full description

Saved in:
Bibliographic Details
Published in:Journal of operator theory 2010-03, Vol.63 (2), p.333-347
Main Authors: BLASCO, OSCAR, POTT, SANDRA
Format: Article
Language:English
Subjects:
Dyadics
Embeddings
Hankel operators
Hilbert spaces
Japanese encephalitis viruses
Martingales
Mathematical vectors
Matrices
Scalars
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We consider BMO spaces of operator-valued functions, among them the space of operator-valued functions B which define a bounded paraproduct on L2(H). We obtain several equivalent formulations of ∥πB∥ in terms of the norm of the "sweep" function of B or of averages of the norms of martingales transforms of B in related spaces. Furthermore, we investigate a connection between John–Nirenberg type inequalities and Carleson-type inequalities via a product formula for paraproducts and deduce sharp dimensional estimates for John–Nirenberg type inequalities.
ISSN:0379-4024
1841-7744