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Weighted restriction theorems for space curves
| Content Provider | Semantic Scholar |
|---|---|
| Author | Bak, Jong-Guk Lee, Jungjin Lee, Sanghyuk |
| Copyright Year | 2007 |
| Abstract | Abstract Consider a nondegenerate C n curve γ ( t ) in R n , n ⩾ 2 , such as the curve γ 0 ( t ) = ( t , t 2 , … , t n ) , t ∈ 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. |
| Starting Page | 1232 |
| Ending Page | 1245 |
| Page Count | 14 |
| File Format | PDF HTM / HTML |
| DOI | 10.1016/j.jmaa.2007.01.039 |
| Alternate Webpage(s) | https://core.ac.uk/download/pdf/82637824.pdf |
| Alternate Webpage(s) | https://doi.org/10.1016/j.jmaa.2007.01.039 |
| Volume Number | 334 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
