A Class of Maximal Functions with Oscillating Kernels

A Class of Maximal Functions with Oscillating Kernels

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摘要 The author studies the L^p mapping properties of a class of maximal functions that are related to oscillatory singular integral operators. Lp estimates, as well as the corresponding weighted estimates of such maximal functions, are obtained. Moreover, several applications of our results are highlighted. The author studies the L^p mapping properties of a class of maximal functions that are related to oscillatory singular integral operators. Lp estimates, as well as the corresponding weighted estimates of such maximal functions, are obtained. Moreover, several applications of our results are highlighted.

作者 Ahmad AL-SALMAN

机构地区 Department of Mathematics

出处《Acta Mathematica Sinica,English Series》 SCIE CSCD 2007年第11期2003-2016,共14页 数学学报（英文版）

关键词 oscillatory singular integrals maximal functions weighted L^p bounds power weights parametric Marcinkiewicz integral operators Morrey spaces oscillatory singular integrals, maximal functions, weighted L^p bounds, power weights,parametric Marcinkiewicz integral operators, Morrey spaces

分类号 O174 [理学—基础数学]

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1Al-Salman, A., Pan, Y.: Singular integrals with rough kernels in L log^+ L(S^n-1). J. London Math. Soc., 66(2), 153-174 (2002)
2Al-Salman, A.: Rough oscillatory singular integral operators of nonconvolution type. J. Math. Anal. Appl., 299, 72-88 (2004)
3Al-Salman, A., Al-Jarrah, A.: Rough Oscillatory Singular Integral Operators-Ⅱ. Turkish. J. Math., 27(4) (2003)
4Al-Salman, A.: On maximal functions with rough kernels in L(logL)^1/2(S^n-1). Collect. Math., 56(1), 47-56 (2005)
5Fan, D., Pan, Y.: Boundedness of certain oscillatory singular integrals. Studia Math., 114, 106-116 (1995)
6Jiang, Y., Lu, S. Z.: Oscillatory singular integrals with rough kernels, M. Cheng et al. (eds.), Harmonic Analysis in China, 135-145
7Lu, S. Z., Zhang, Y.: Criteriou on L^p -boundedness for a class of oscillatory singular integrals with rough kernels. Rev. Math. Iberoamericana, 8, 201-219 (1992)
8Pan, Y.: L^2 estimates for convolution operators with oscillating kernels. Math. Proc. Phil. Soc., 113, 179-193 (1993)
9Ricci, F., Stein, E. M.: Harmonic analysis on nilpotent groups and singular integrals Ⅰ: Oscillatory integrals. J. Funct. Anal., 73, 179-194 (1987)
10Sjolin, P.: Convolution with oscillating kernels. Indiana U. Math. J., 30, 47-56 (1981)

1江寅生,陆善镇.关于粗糙核振荡奇异积分的一个注记[J].北京师范大学学报（自然科学版）,1991,27(4):398-402.
2邱启荣.振荡奇异积分的L^p有界性[J].数学学报（中文版）,1997,40(1):129-132.
3ZHAO Kai,WANG Lei.Boundedness of a Kind of Oscillatory Singular Integral Operators[J].Chinese Quarterly Journal of Mathematics,2009,24(4):598-604.
4李晓春.伴随Herz空间的Hardy空间上的振荡奇异积分[J].北京师范大学学报（自然科学版）,1996,32(4):427-432.
5Yurong WU,Shiliang ZHAO.A Note on the Maximal Functions on Weighted Harmonic AN Groups[J].Chinese Annals of Mathematics,Series B,2016,37(2):193-198.
6于湖波,赵凯,姜诺,席芳,张红俊.振荡奇异积分算子在Herz型空间的有界性[J].青岛大学学报（自然科学版）,2012,25(4):12-15.
7胡国恩,杨大春.Hardy空间上的多线性振荡奇异积分算子[J].数学年刊（A辑）,1997,1(5):569-578.
8杨大春,周祖胜.Haray空间上的某些振荡奇异积分[J].北京师范大学学报（自然科学版）,1998,34(4):427-432.
9勒孚龙,胡国恩.一类振荡奇异积分(英文)[J].Journal of Mathematical Research and Exposition,1999,19(1):18-24.
10江寅生.粗糙核振荡奇异积分L^p有界性的一个判别准则[J].新疆大学学报（自然科学版）,1994,11(4):52-55. 被引量：1

Acta Mathematica Sinica,English Series

2007年第11期

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A Class of Maximal Functions with Oscillating Kernels

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