Logarithmic Mean Oscillation on the Polydisc, Multi-Parameter Paraproducts and Iterated Commutators

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Abstract

We introduce another notion of bounded logarithmic mean oscillation in the N-torus and give an equivalent definition in terms of boundedness of multi-parameter paraproducts from the dyadic little BMO, bmod(TN) to the dyadic product BMO space, BMOd(TN). We also obtain a sufficient condition for the boundedness of the iterated commutators from the subspace of bmo(ℝN) consisting of functions with support in [0,1]N to BMO(ℝN).

Original languageEnglish
Pages (from-to)500-523
Number of pages24
JournalJournal of Fourier Analysis and Applications
Volume20
Issue number3
DOIs
Publication statusPublished - Jun 2014
Externally publishedYes

Keywords

  • Bounded mean oscillation
  • Haar basis
  • Logarithmic mean oscillation
  • Paraproduct
  • Product domains

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