Rough oscillatory singular integrals on ℝⁿ
| Author | Al-Qassem, Hussain Mohammad |
| Author | Cheng, Leslie |
| Author | Pan, Yibiao |
| Available date | 2024-02-06T07:02:18Z |
| Publication Date | 2014-01-01 |
| Publication Name | Studia Mathematica |
| Identifier | http://dx.doi.org/10.4064/sm221-3-4 |
| Citation | Al-Qassem, H., Cheng, L., & Pan, Y. (2014). Rough oscillatory singular integrals on ℝⁿ. Studia Mathematica, 3(221), 249-267. |
| ISSN | 00393223 |
| Abstract | We establish sharp bounds for oscillatory singular integrals with an arbitrary real polynomial phase P. The kernels are allowed to be rough both on the unit sphere and in the radial direction. We show that the bounds grow no faster than log deg(P), which is optimal and was first obtained by Papadimitrakis and Parissis (2010) for kernels without any radial roughness. Among key ingredients of our methods are an L1 → L2 estimate and extrapolation. |
| Language | en |
| Publisher | Instytut Matematyczny |
| Subject | Block spaces Extrapolation L boundedness p Orlicz spaces Oscillatory singular integral Rough kernel Singular integral |
| Type | Article |
| Pagination | 249-267 |
| Issue Number | 3 |
| Volume Number | 221 |
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Mathematics, Statistics & Physics [676 items ]