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L^p-boundedness for the commutators of rough oscillatory singular integrals with non-convolution phases

Huoxiong Wu
대한수학회 (The Korean Mathematical Society)|2009.05|대한수학회지 (Journal of the KMS)|제46권 제3호|pp. 577-588

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참고문헌

키워드

commutatorrough kerneloscillatory singular integralBMO(R^n)
주제분류수학

초록

In this paper, the author studies the k-th commutators of oscillatory singular integral operators with a BMO function and phases more general than polynomials. For 1<p<∞, the L^p-boundedness of such operators are obtained provided their kernels belong to the spaces L((log^+)L)^{k+1}(S^{n-1}). The results of the corresponding maximal operators are also established.

Abstract

In this paper, the author studies the k-th commutators of oscillatory singular integral operators with a BMO function and phases more general than polynomials. For 1<p<∞, the L^p-boundedness of such operators are obtained provided their kernels belong to the spaces L((log^+)L)^{k+1}(S^{n-1}). The results of the corresponding maximal operators are also established.

참고문헌 (15)

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  9. S. Lu, "Oscillatory singular integrals and commutators with rough kernels", Ann. Sci. Math. Quebec, 27(1), pp.47~66 (2003)
  10. S. Lu, "Criterion on Lp-boundedness for a class of oscillatory singular integrals with rough kernels", Rev. Mat. Iberoamericana, 8(2), pp.201~219 (1992)
  11. B. Ma, "L2(Rn) boundedness for commutators of oscillatory singular integral operators", Approx. Theory Appl., 16(2), pp.37~44 (2000)
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  15. H. Wu, "Boundedness of higher order commutators of oscillatory singular integrals with rough kernels", Studia Math., 167(1), pp.29~43 (2005)

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