LP-Boundedness of the Multiple Hilbert Transform Along a Surface

Document Type

Article

Publication Date

9-1-1983

Identifier/URL

40974821 (Pure)

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.

DOI

10.2140/pjm.1983.108.221

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