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Weighted restriction theorems for space curves
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- Title
- Weighted restriction theorems for space curves

- Date Issued
- 2007-10-15

- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE

- Abstract
- Consider a nondegenerate C-n curve gamma(t) in R-n, n >= 2, such as the curve gamma(0)(t) = (t, t(2),..., t(n)), t epsilon I, where I is an interval in R. We first prove a weighted Fourier restriction theorem for such curves, with a weight in a Wiener amalgam space, for the full range of exponents p, q, when I is a finite interval. Next, we obtain a generalization of this result to some related oscillatory integral operators. In particular, our results suggest that this is a quite general phenomenon which occurs, for instance, when the associated oscillatory integral operator acts on functions f with a fixed compact support. Finally, we prove an analogue, for the Fourier extension operator (i.e. the adjoint of the Fourier restriction operator), of the two-weight norm inequality of B. Muckenhoupt for the Fourier transform. Here I may be either finite or infinite. These results extend two results of J. Lakey on the plane to higher dimensions. (c) 2007 Elsevier Inc. All rights reserved.

- Keywords
- Fourier restriction theorem; oscillatory integral operator; amalgam space; weighted norm inequality; FOURIER RESTRICTION; DEGENERATE CURVES; HARMONIC-ANALYSIS; TRANSFORM; AMALGAMS; LP; LQ

- ISSN
- 0022-247X

- Article Type
- Article

- Citation
- JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol. 334, no. 2, page. 1232 - 1245, 2007-10-15

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- 박종국BAK, JONG GUK
- Dept of Mathematics

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