Tohoku Mathematical Journal
2005
March
SECOND SERIES VOL. 57, NO. 1

Tohoku Math. J.
57 (2005), 119-145

Title THE DYADIC STRUCTURE AND ATOMIC DECOMPOSITION OF $Q$ SPACES IN SEVERAL REAL VARIABLES

Author Galia Dafni and Jie Xiao

(Received June 10, 2003, revised May 6, 2004)
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.

2000 Mathematics Subject Classification. Primary 42B35;Secondary 46E30, 47B38.
Key words and phrases. $Q$ spaces, BMO, dyadic structure, martingales, fractional Carleson measures, atomic decomposition, quasi-orthogonal decomposition.

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