Logarithmic Mean Oscillation on the Polydisc,Multi-Parameter Paraproducts and Iterated Commutators |
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Authors: | Benoît F Sehba |
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Institution: | 1. Département de Mathématiques, Faculté des Sciences, Université de Yaoundé I, B. P. 812, Yaoundé, Cameroon
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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 \(\mathrm {BMO}\) , \(\mathrm {bmo}^d(\mathbb {T}^N)\) to the dyadic product \(\mathrm {BMO}\) space, \(\mathrm {BMO}^d(\mathbb {T}^N)\) . We also obtain a sufficient condition for the boundedness of the iterated commutators from the subspace of \(\mathrm {bmo}(\mathbb {R}^N)\) consisting of functions with support in \(0,1]^N\) to \(\mathrm {BMO}(\mathbb {R}^N)\) . |
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