Double Hilbert transform along real-analytic surfaces in d+2

Malabika Pramanik; Chan Woo Yang

doi:10.1112/jlms/jdm113

Double Hilbert transform along real-analytic surfaces in ^d+2

Malabika Pramanik, Chan Woo Yang

Department of Mathematics

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

4 Citations (Scopus)

Abstract

We give a necessary and sufficient condition for the double Hilbert transform on ^d+2 to be bounded on L^p, 1 < p < ∞. This generalizes a result of Carbery, Wainger and Wright [Duke Math. J. 101 (2000) 499-513] for d = 1.

Original language	English
Pages (from-to)	363-386
Number of pages	24
Journal	Journal of the London Mathematical Society
Volume	77
Issue number	2
DOIs	https://doi.org/10.1112/jlms/jdm113
Publication status	Published - 2008 Apr

ASJC Scopus subject areas

Mathematics(all)

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10.1112/jlms/jdm113

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title = "Double Hilbert transform along real-analytic surfaces in d+2",

abstract = "We give a necessary and sufficient condition for the double Hilbert transform on d+2 to be bounded on Lp, 1 < p < ∞. This generalizes a result of Carbery, Wainger and Wright [Duke Math. J. 101 (2000) 499-513] for d = 1.",

author = "Malabika Pramanik and Yang, {Chan Woo}",

note = "Funding Information: Received 30 January 2005; revised 19 December 2006; published online 12 February 2008. 2000 Mathematics Subject Classification 44A15, 42B15, 42B20. Research of the first author supported in part by NSF grant DMS-0443322.",

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AB - We give a necessary and sufficient condition for the double Hilbert transform on d+2 to be bounded on Lp, 1 < p < ∞. This generalizes a result of Carbery, Wainger and Wright [Duke Math. J. 101 (2000) 499-513] for d = 1.

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Double Hilbert transform along real-analytic surfaces in ^d+2

Abstract

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