Multilinear extrapolation and applications to the bilinear Hilbert transform

DOI10.1016/j.jmaa.2009.04.021zbMath1168.47003OpenAlexW1986007983MaRDI QIDQ1029118

Fernando Soria, María Jesús Carro, Loukas Grafakos, José Maria Martell

Publication date: 9 July 2009

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2009.04.021

zbMATH Keywords

bilinear Hilbert transform\((\varepsilon\delta)\)-atomic operatorsgalbmultilinear extrapolationrestricted weak type estimates

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Several-variable operator theory (spectral, Fredholm, etc.) (47A13) Abstract interpolation of topological vector spaces (46M35) Forms (bilinear, sesquilinear, multilinear) (47A07)

Related Items (4)

Upper endpoint estimates and extrapolation for commutators ⋮ Endpoint bounds for the quartile operator ⋮ Lacunary Fourier and Walsh-Fourier series near \(L^1\) ⋮ Endpoint bounds for the bilinear Hilbert transform

Cites Work

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• Distributional estimates for the bilinear Hilbert transform
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• Restricted weak type versus weak type
• Remarks on a theorem by N. Yu. Antonov
• FROM RESTRICTED WEAK TYPE TO STRONG TYPE ESTIMATES
• On an extrapolation theorem of Carleson-Sjölin type with applications to a.e. convergence of Fourier series
• From restricted type to strong type estimates on quasi-Banach rearrangement invariant spaces
• On Restricted Weak Type (1, 1)

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