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

Benoît F. Sehba

doi:10.1007/s00041-014-9325-6

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

Benoît F. Sehba

Université de Yaoundé I

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

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, bmo^d(T^N) to the dyadic product BMO space, BMO^d(T^N). We also obtain a sufficient condition for the boundedness of the iterated commutators from the subspace of bmo(ℝ^N) consisting of functions with support in [0,1]^N to BMO(ℝ^N).

Original language	English
Pages (from-to)	500-523
Number of pages	24
Journal	Journal of Fourier Analysis and Applications
Volume	20
Issue number	3
DOIs	https://doi.org/10.1007/s00041-014-9325-6
Publication status	Published - Jun 2014
Externally published	Yes

Keywords

Bounded mean oscillation
Haar basis
Logarithmic mean oscillation
Paraproduct
Product domains

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10.1007/s00041-014-9325-6

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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).",

keywords = "Bounded mean oscillation, Haar basis, Logarithmic mean oscillation, Paraproduct, Product domains",

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year = "2014",

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doi = "10.1007/s00041-014-9325-6",

language = "English",

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T1 - Logarithmic Mean Oscillation on the Polydisc, Multi-Parameter Paraproducts and Iterated Commutators

AU - Sehba, Benoît F.

PY - 2014/6

Y1 - 2014/6

N2 - 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).

AB - 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).

KW - Bounded mean oscillation

KW - Haar basis

KW - Logarithmic mean oscillation

KW - Paraproduct

KW - Product domains

UR - https://www.scopus.com/pages/publications/84902364619

U2 - 10.1007/s00041-014-9325-6

DO - 10.1007/s00041-014-9325-6

M3 - Article

AN - SCOPUS:84902364619

SN - 1069-5869

VL - 20

SP - 500

EP - 523

JO - Journal of Fourier Analysis and Applications

JF - Journal of Fourier Analysis and Applications

IS - 3

ER -

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

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Keywords

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