Browse > Article
http://dx.doi.org/10.4134/JKMS.2009.46.3.577

Lp-BOUNDEDNESS FOR THE COMMUTATORS OF ROUGH OSCILLATORY SINGULAR INTEGRALS WITH NON-CONVOLUTION PHASES  

Wu, Huoxiong (SCHOOL OF MATHEMATICAL SCIENCES XIAMEN UNIVERSITY)
Publication Information
Journal of the Korean Mathematical Society / v.46, no.3, 2009 , pp. 577-588 More about this Journal
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 < $\infty$, 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.
Keywords
commutator; oscillatory singular integral; BMO($\mathbb{R}^2$); rough kernel;
Citations & Related Records

Times Cited By Web Of Science : 0  (Related Records In Web of Science)
Times Cited By SCOPUS : 1
연도 인용수 순위
1 Y. Ding and S. Lu, Weighted Lp-boundedness for higher order commutators of oscillatory singular integrals, Tohoku Math. J. (2) 48 (1996), no. 3, 437–449   DOI
2 G. Hu, Weighted norm inequalities for commutators of homogeneous singular integrals, A Chinese summary appears in Acta Math. Sinica 39 (1996), no. 1, 141; Acta Math. Sinica (N.S.) 11 (1995), Special Issue, 77–88
3 G. Hu, $L^p(R^n)$ boundedness for the commutator of a homogeneous singular integral operator, Studia Math. 154 (2003), no. 1, 13–27
4 Y. Jiang and S. Lu, Oscillatory singular integrals with rough kernel, Harmonic analysis in China, 135–145, Math. Appl., 327, Kluwer Acad. Publ., Dordrecht, 1995
5 A. Al-Salman, Rough oscillatory singular integral operators of nonconvolution type, J. Math. Anal. Appl. 299 (2004), no. 1, 72–88   DOI   ScienceOn
6 Y. Ding, Some problems on oscillatory singular integral and fractional integral with rough kernel, Ph. D. Thesis, Beijing Normal Univ., 1995
7 E. M. Stein, Problems in harmonic analysis related to curvature and oscillatory integrals, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986), 196–221, Amer. Math. Soc., Providence, RI, 1987
8 S. Lu and H. Wu, Oscillatory singular integrals and commutators with rough kernels, Ann. Sci. Math. Quebec 27 (2003), no. 1, 47–66
9 S. Lu and Y. Zhang, Criterion on Lp-boundedness for a class of oscillatory singular integrals with rough kernels, Rev. Mat. Iberoamericana 8 (1992), no. 2, 201–219
10 F. Ricci and E. M. Stein, Harmonic analysis on nilpotent groups and singular integrals. I. Oscillatory integrals, J. Funct. Anal. 73 (1987), no. 1, 179–194   DOI
11 H. Wu, Boundedness of higher order commutators of oscillatory singular integrals with rough kernels, Studia Math. 167 (2005), no. 1, 29–43
12 E. M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality and Oscillatory Integrals, Princeton University Press, Princeton, NJ, 1993
13 A. Al-Salman and A. Al-Jarrah, Rough oscillatory singular integral operators. II, Turkish J. Math. 27 (2003), no. 4, 565–579
14 S. Lu, M. Taibleson, and G. Weiss, Spaces Generated by Blocks, Beijing Normal University Press, Beijing, 1989
15 B. Ma and G. Hu, $L^2(R^n)$ boundedness for commutators of oscillatory singular integral operators, Approx. Theory Appl. (N.S.) 16 (2000), no. 2, 37–44   DOI