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

Sandra Pott; Benoît Sehba

doi:10.1007/s11854-012-0012-8

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

Sandra Pott
, Benoît Sehba

Department of Mathematics

Lund University

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We study boundedness properties of a class ofmultiparameter paraproducts on the dual space of the dyadic Hardy space H_d¹ (T^N), the dyadic product BMO space BMO^d (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).

Original language	English
Pages (from-to)	1-27
Number of pages	27
Journal	Journal d'Analyse Mathematique
Volume	117
Issue number	1
DOIs	https://doi.org/10.1007/s11854-012-0012-8
Publication status	Published - Jun 2012

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abstract = "We study boundedness properties of a class ofmultiparameter paraproducts on the dual space of the dyadic Hardy space Hd1 (TN), the dyadic product BMO space BMOd (TN). 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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AU - Pott, Sandra

AU - Sehba, Benoît

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N2 - We study boundedness properties of a class ofmultiparameter paraproducts on the dual space of the dyadic Hardy space Hd1 (TN), the dyadic product BMO space BMOd (TN). 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).

AB - We study boundedness properties of a class ofmultiparameter paraproducts on the dual space of the dyadic Hardy space Hd1 (TN), the dyadic product BMO space BMOd (TN). 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).

UR - https://www.scopus.com/pages/publications/84863322009

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DO - 10.1007/s11854-012-0012-8

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

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