Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


On the restriction of the Fourier transform to curves: endpoint results and the degenerate case

Author: Michael Christ
Journal: Trans. Amer. Math. Soc. 287 (1985), 223-238
MSC: Primary 42B10; Secondary 26A33
MathSciNet review: 766216
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For smooth curves $ \Gamma $ in $ {{\mathbf{R}}^n}$ with certain curvature properties it is shown that the composition of the Fourier transform in $ {{\mathbf{R}}^n}$ followed by restriction to $ \Gamma $ defines a bounded operator from $ {L^p}({{\mathbf{R}}^n})$ to $ {L^q}(\Gamma )$ for certain $ p,q$. The curvature hypotheses are the weakest under which this could hold, and $ p$ is optimal for a range of $ q$. In the proofs the problem is reduced to the estimation of certain multilinear operators generalizing fractional integrals, and they are treated by means of rearrangement inequalities and interpolation between simple endpoint estimates.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 42B10, 26A33

Retrieve articles in all journals with MSC: 42B10, 26A33

Additional Information

PII: S 0002-9947(1985)0766216-6
Keywords: Fourier transform, curvature, multilinear operator, interpolation
Article copyright: © Copyright 1985 American Mathematical Society