A class of oscillatory singular integrals with rough kernels and fewnomials phases. (English) Zbl 1540.42031
Let \(Q(t):=\sum_{1\leq i \leq m}a_i t^{\alpha_i}\) be a real-valued polynomial, \(\Omega\) be a homogenous function of degree zero with mean value zero on the unit sphere. The oscillatory singular integral operator \(T_Q\) is defined by
\[
T_{Q}(f)(x):=p.v. \int_{\mathbb{R}^n }f(x-y) \frac{\Omega(y)}{|y|^n} e^{iQ(|y|)} \,\textrm{d}y .
\]
In this paper, the authors prove the \(L^p(\omega)\) boundedness of \(T_{Q}\) for \(1<p<\infty\) and \(\omega\in A^{I}_p(\mathbb{R}_+)\). Some similar results can be found in [S. Guo, New York J. Math. 2017, 1733–1738 (2017; Zbl 1388.42038)].
Reviewer: Haixia Yu (Beijing)
MSC:
| 42B20 | Singular and oscillatory integrals (Calderón-Zygmund, etc.) |
| 42B25 | Maximal functions, Littlewood-Paley theory |
Citations:
Zbl 1388.42038References:
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