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Logarithmic mean oscillation on the polydisc, endpoint results for multi-parameter paraproducts, and commutators on BMO

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Abstract

We study boundedness properties of a class ofmultiparameter paraproducts on the dual space of the dyadic Hardy space H 1 d (T N), the dyadic product BMO space BMOd (T N). For this, we introduce a notion of logarithmic mean oscillation on the polydisc. We also obtain a result on the boundedness of iterated commutators on BMO [0, 1]N).

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Authors and Affiliations

  1. Centre for Mathematical Sciences Faculty of Science, Lund University, 22100, Lund, Sweden

    Sandra Pott

  2. School of Mathematics Trinity College, Dublin 2, Ireland

    Benoît Sehba

  3. Centre de Mathématiques et Informatique, Université Aix-Marseille I, 39, Rue Joliot Curie, 13453, Marseille Cedex 13, France

    Benoît Sehba

Authors
  1. Sandra Pott
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  2. Benoît Sehba
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Correspondence to Benoît Sehba.

Additional information

supported by a Heisenberg fellowship of the German Research Foundation (DFG)

received funding from the “Irish Research Council for Science, Engineering and Technology”

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Pott, S., Sehba, B. Logarithmic mean oscillation on the polydisc, endpoint results for multi-parameter paraproducts, and commutators on BMO. JAMA 117, 1–27 (2012). https://doi.org/10.1007/s11854-012-0012-8

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  • DOI: https://doi.org/10.1007/s11854-012-0012-8

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