Double Hilbert transform along real-analytic surfaces in ℝ<sup> <i>d</i> +2</sup>

Malabika Pramanik, Chan Woo Yang

Type: Article

Publication Date: 2008-02-12

Citations: 5

DOI: https://doi.org/10.1112/jlms/jdm113

Abstract

ABSTRACT We give a necessary and sufficient condition for the double Hilbert transform on ℝ 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.

Locations

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Works Cited by This (6)

Action	Title	Year	Authors
+	Singular Integrals and Differentiability Properties of Functions.	1971	Elias M. Stein
+	Singular integrals and the Newton diagram	2006	Anthony Carbery Stephen Wainger James Wright
+	Weak-type estimate for a maximal function	2006	S. K. Patel
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+	Maximal and singular integral operators via Fourier transform estimates	1986	Javier Duoandikoetxea J.-L. Rubio de Francia
+	Double Hilbert transforms along polynomial surfaces in ℝ3	2000	Anthony Carbery Stephen Wainger James Wright