Tohoku Mathematical Journal

The dyadic structure and atomic decomposition of {$Q$} spaces in several real variables

Galia Dafni and Jie Xiao

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Abstract

This paper contains several results relating $Q$ spaces in several real variables with their dyadic counterparts, which are analogues of theorems for BMO and for $Q$ spaces on the circle. In addition, it gives an atomic (or quasi-orthogonal) decomposition for these $Q$ spaces in terms of the same type of atoms used to decompose BMO.

Article information

Source
Tohoku Math. J. (2), Volume 57, Number 1 (2005), 119-145.

Dates
First available in Project Euclid: 11 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1113234836

Digital Object Identifier
doi:10.2748/tmj/1113234836

Mathematical Reviews number (MathSciNet)
MR2113992

Zentralblatt MATH identifier
1129.42400

Subjects
Primary: 42B35: Function spaces arising in harmonic analysis
Secondary: 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 47B38: Operators on function spaces (general)

Keywords
Q spaces BMO dyadic structure martingales fractional Carleson measures atomic decomposition quasi-orthogonal decomposition

Citation

Dafni, Galia; Xiao, Jie. The dyadic structure and atomic decomposition of {$Q$} spaces in several real variables. Tohoku Math. J. (2) 57 (2005), no. 1, 119--145. doi:10.2748/tmj/1113234836. https://projecteuclid.org/euclid.tmj/1113234836


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