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Journal of the London Mathematical Society Advance Access originally published online on February 12, 2008
Journal of the London Mathematical Society 2008 77(2):363-386; doi:10.1112/jlms/jdm113
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© 2008 London Mathematical Society

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

Malabika Pramanik

Department of Mathematics
University of British Columbia
Vancouver, BC V6T 1Z2
Canada

Chan Woo Yang

Department of Mathematics
Korea University
Seoul 136-701
Republic of Korea
cw_yang@korea.ac.kr

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

2000 Mathematics Subject Classification 44A15, 42B15, 42B20.

Research of the first author supported in part by NSF grant DMS-0443322.

Received January 30, 2005; revised December 19, 2006; published online February 12, 2008.


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