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Abstract
We prove that the multiparameter (product) space BMO of functions of bounded mean oscillation can be written as the intersection of finitely many dyadic product BMO spaces, with equivalent norms, generalizing the oneparameter result of T. Mei. We establish the analogous dyadic structure theorems for the space VMO of functions of vanishing mean oscillation, for Ap weights, for reverseHölder weights and for doubling weights. We survey several definitions of VMO and prove their equivalences, in the continuous, dyadic, oneparameter and product cases. In particular, we introduce the space of dyadic product VMO functions. We show that the weighted product Hardy space H_{ω}^{1} is the sum of finitely many translates of dyadic weighted H_{ω}^{1}, for each A∞ weight ω, and that the weighted strong maximal function is pointwise comparable to the sum of finitely many dyadic weighted strong maximal functions, for each doubling weight ω. Our results hold in both the compact and noncompact cases.
Original language  English 

Pages (fromto)  767797 
Number of pages  31 
Journal  Revista Matematica Iberoamericana 
Volume  31 
Issue number  3 
DOIs  
Publication status  Published  2015 
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Dive into the research topics of 'Dyadic structure theorems for multiparameter function spaces'. Together they form a unique fingerprint.Projects
 1 Finished

Harmonic analysis: Function spaces and singular integral operators
13/02/12 → 31/12/17
Project: Research