A multilinear generalisation of the Hilbert transform and fractional integration
type: Item
instance of: scholarly article
title: A multilinear generalisation of the Hilbert transform and fractional integration
zbMATH Open document ID: 1248.44006
DOI: 10.4171/RMI/665
author: Stefán Ingi Valdimarsson
published in: Revista Matemática Iberoamericana
publication date: 2012-03-03T00:00:00Z
review text: The Hilbert transform and a fractional integral operator can be considered as convolution operators which calculate a certain volume in \(\mathbb{R}\). The author extends these operators to higher dimensions by mutilinearizing them in two ways.
reviewed by: Mehmet Cenkci
Mathematics Subject Classification ID: 44A15
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 45P05
zbMATH DE Number: 6011504
zbMATH Keywords: Hilbert transform
zbMATH Keywords: fractional integration
zbMATH Keywords: multilinear operator
zbMATH Keywords: best constant
zbMATH Keywords: fractional integral operator
zbMATH Keywords: convolution operators
MaRDI profile type: Publication
cites work: Some conjectures aboutLp norms of k-plane transforms
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cites work: A general rearrangement inequality for multiple integrals
cites work: Cases of equality in the Riesz rearrangement inequality
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full work available at URL: https://doi.org/10.4171/rmi/665
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description: scientific article; zbMATH DE number 6011504