Restrictions of Fourier transforms to curves

S.W. Drury

Type: Article

Publication Date: 1985-01-01

Citations: 67

DOI: https://doi.org/10.5802/aif.1001

Abstract

Let x(t)=(t,1 2t 2 ,1 6t 3 ) a certain curve in R 3 . We investigate inequalities of the type {∫|f ^(x(t))| b dt} 1/b ≤C∥f∥ a for f∈𝒮(R 3). Our results improve improve an earlier restriction theorem of Prestini. Various generalizations are also discussed.

Locations

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Works Cited by This (5)

Action	Title	Year	Authors
+	Introduction to Fourier Analysis on Euclidean Spaces.	1971	Elias M. Stein Guido Weiss
+ PDF Chat	A restriction theorem for space curves	1978	Elena Prestini
+ PDF Chat	A Restriction Theorem for Space Curves	1978	E. Prestini
+	Differential Geometry	1961
+ PDF Chat	On Fourier coefficients and transforms of functions of two variables	1974	A. Zygmund