An estimate on the Bedrosian commutator in Sobolev space

While the Bedrosian identity for the Hilbert transform of a product does not hold for general Sobolev class functions, we show that the defect of this identity is more regular than would be naively expected. We use this result to give a stronger-than-expected estimate on the chain rule defect of the...

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Detalles Bibliográficos
Autor principal: Oliver, Marcel
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6297168/
https://www.ncbi.nlm.nih.gov/pubmed/30839881
http://dx.doi.org/10.1186/s13660-018-1940-3
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author Oliver, Marcel
author_facet Oliver, Marcel
author_sort Oliver, Marcel
collection PubMed
description While the Bedrosian identity for the Hilbert transform of a product does not hold for general Sobolev class functions, we show that the defect of this identity is more regular than would be naively expected. We use this result to give a stronger-than-expected estimate on the chain rule defect of the square root of the Laplacian.
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spelling pubmed-62971682018-12-28 An estimate on the Bedrosian commutator in Sobolev space Oliver, Marcel J Inequal Appl Research While the Bedrosian identity for the Hilbert transform of a product does not hold for general Sobolev class functions, we show that the defect of this identity is more regular than would be naively expected. We use this result to give a stronger-than-expected estimate on the chain rule defect of the square root of the Laplacian. Springer International Publishing 2018-12-17 2018 /pmc/articles/PMC6297168/ /pubmed/30839881 http://dx.doi.org/10.1186/s13660-018-1940-3 Text en © The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Oliver, Marcel
An estimate on the Bedrosian commutator in Sobolev space
title An estimate on the Bedrosian commutator in Sobolev space
title_full An estimate on the Bedrosian commutator in Sobolev space
title_fullStr An estimate on the Bedrosian commutator in Sobolev space
title_full_unstemmed An estimate on the Bedrosian commutator in Sobolev space
title_short An estimate on the Bedrosian commutator in Sobolev space
title_sort estimate on the bedrosian commutator in sobolev space
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6297168/
https://www.ncbi.nlm.nih.gov/pubmed/30839881
http://dx.doi.org/10.1186/s13660-018-1940-3
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