Vol. 108, No. 1, 1983

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ISSN: 0030-8730
Lp-boundedness of the multiple Hilbert transform along a surface

James Thomas Vance, Jr.

Vol. 108 (1983), No. 1, 221–241
Abstract

For an appropriate surface σ in Rn, we prove that the multiple Hilbert transform along σ is a bounded operator on Lp(Rn), for p sufficiently close to 2. Our analysis of this singular integral operator proceeds via Fourier transform techniques—that is, on the “multiplier side”—with applications of Stein’s analytic interpolation theorem and the Marcinkiewicz multiplier theorem. At the heart of our argument we have estimates of certain trigonometric integrals.

Mathematical Subject Classification 2000
Primary: 44A15
Secondary: 42B20
Milestones
Received: 1 November 1981
Published: 1 September 1983
Authors
James Thomas Vance, Jr.