\(L^p\) bounds for the commutators of oscillatory singular integrals with rough kernels. (English) Zbl 1472.42016

Chen, Yanping; Zhu, Kai

Abstr. Appl. Anal. 2014, Article ID 393147, 8 p. (2014).

Summary: We establish the \(L^p\) boundedness for some commutators of oscillatory singular integrals with the kernel condition which was introduced by L. Grafakos and A. Stefanov [Indiana Univ. Math. J. 47, No. 2, 455–469 (1998; Zbl 0913.42014)]. Our theorems contain various conditions on the phase function.

MSC:

42B20	Singular and oscillatory integrals (Calderón-Zygmund, etc.)
42B25	Maximal functions, Littlewood-Paley theory

Keywords:

method of rotations; Calderón-Zygmund singular integral operators; rough homogeneous kernels; maximal singular integrals

Citations:

Zbl 0913.42014

References:

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