On Certain Estimates Of Rough Oscillatory Singular Integrals
We obtain appropriate sharp estimates for rough oscillatory integrals. Our results represent significant improvements as well as natural extensions of what was known previously.
[1] A. Al-Salman and Y. Pan, Singular integrals with rough kernels, Canad. Math. Bull. 47 (2004), no. 1, 3-11.
[2] H. M. Al-Qassem, L. Cheng, and Y. Pan, On the boundedness of rough oscillatory singular integrals on Trieble-Lizorkin spaces. To appear in Acta Mathematica Sinica.
[3] H. M. Al-Qassem, L. Cheng, A. Fukui and Y. Pan, Bounds for Oscilla¬tory Singular Integrals on Rn. To appear in Math. Nachrichten J.
[4] G. I. Arkhipov, A. A. Karacuba, and V. N. Cubarikov, Trigonometric integrals, Izv. Akad. Nauk SSSR Ser. Mat. 43 (1979), no. 5, 971-1003, 1197.
[5] A. Carbery and J. Wright, Distributional and Lq norm inequalities for polynomials over convex bodies in Rn, Math. Res. Lett. 8 (2001), no. 3, 233-248.
[6] R. Coifman and G. Weiss, Extension of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569-645.
[7] L. Grafakos and A. Stefanov, LP bounds for singular integrals and maximal singular integrals with rough kernel, Indiana Univ. Math. J, whi
47 (1998), 455-469.
[8] I. R. Parissis, Oscillatory Integrals with Polynomial Phase, Ph. D Thesis, University of Crete, 2007.
[9] M. Padimitrakis and I. R. Parissis, Singular oscillatory integrals on Rn, Math. Z., to appear.
[10] E. M. Stein, Oscillatory integrals in Fourier analysis, Beijing lectures in harmonic analysis (Beijing, 1984), Ann. of Math. Stud., vol. 112, Princeton Univ. Press, Princeton, NJ, 1986, p. 307-355.
[11] Elias M. Stein and Stephen Wainger, The estimation of an integral arising in multiplier transformations, Studia Math. 35 (1970), 101-104.
[1] A. Al-Salman and Y. Pan, Singular integrals with rough kernels, Canad. Math. Bull. 47 (2004), no. 1, 3-11.
[2] H. M. Al-Qassem, L. Cheng, and Y. Pan, On the boundedness of rough oscillatory singular integrals on Trieble-Lizorkin spaces. To appear in Acta Mathematica Sinica.
[3] H. M. Al-Qassem, L. Cheng, A. Fukui and Y. Pan, Bounds for Oscilla¬tory Singular Integrals on Rn. To appear in Math. Nachrichten J.
[4] G. I. Arkhipov, A. A. Karacuba, and V. N. Cubarikov, Trigonometric integrals, Izv. Akad. Nauk SSSR Ser. Mat. 43 (1979), no. 5, 971-1003, 1197.
[5] A. Carbery and J. Wright, Distributional and Lq norm inequalities for polynomials over convex bodies in Rn, Math. Res. Lett. 8 (2001), no. 3, 233-248.
[6] R. Coifman and G. Weiss, Extension of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569-645.
[7] L. Grafakos and A. Stefanov, LP bounds for singular integrals and maximal singular integrals with rough kernel, Indiana Univ. Math. J, whi
47 (1998), 455-469.
[8] I. R. Parissis, Oscillatory Integrals with Polynomial Phase, Ph. D Thesis, University of Crete, 2007.
[9] M. Padimitrakis and I. R. Parissis, Singular oscillatory integrals on Rn, Math. Z., to appear.
[10] E. M. Stein, Oscillatory integrals in Fourier analysis, Beijing lectures in harmonic analysis (Beijing, 1984), Ann. of Math. Stud., vol. 112, Princeton Univ. Press, Princeton, NJ, 1986, p. 307-355.
[11] Elias M. Stein and Stephen Wainger, The estimation of an integral arising in multiplier transformations, Studia Math. 35 (1970), 101-104.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:61332", author = "H. M. Al-Qassem", title = "On Certain Estimates Of Rough Oscillatory Singular Integrals", abstract = "We obtain appropriate sharp estimates for rough oscillatory integrals. Our results represent significant improvements as well as natural extensions of what was known previously.
", keywords = "Oscillatory singular integral, Rough kernel, Singular integral, L^{p} boundedness.", volume = "5", number = "3", pages = "472-4", }
