振蕩奇異積分算子在herz型空間的有界性大論-資料下載頁
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【正文】 i 2kj /1 ????? pKzi i pqfc ,||)||(|| /1 ??? ???? pqKpqK gg ?????? ? , ||||||sup 1|||| ?? pKzi i pqfc ,||)||(|| /1 ??? ???? 綜上所述，引理 得到證明 . 定理的證明 定理 的證明 : 由引理 得 pqpqspq Kzj jsjbKzj bjsjFKb fTfTfT , ||)|)2(|(||||)||2(|||||| /1/1 ???? ????? ?? ??? ?? ? ?? ? ???? pqKj jsj fc ,||)||2(|| /1 ???? ? ?? ?? ? spq FKfc ??,|||| ??. 定理 的證明 : 由引理 得 ????? ???? ??/1/1 )||)2(||()||||2(|||| , ?? ???? ??j KjsjbKbjjsjBKb pqpqspq fTfTfT ??? ??? ?? /1)||||2( ,? ?? ?j Kjsj pqfc ? spq BKfc ??,|||| ??. 參考文獻 [1] Ricci F, Stein E analysis on nilpotent groups and singular integrals, I. Oscillatory integrals[J].J. Funct. ,73(1): 179–194. [2] Chanillo S,Christ M. Weak (1, 1) bounds for oscillatory singular integrals[J]. Duke Math. J. 1987,55(1):141–155. [3] LU on Lpboundedness for a class of oscillatory singular integrals with rough kernels[J]. Rev. Mat. ,8:201–219. [4] estimates for rough oscillatory singular integrals[J].J. Fourier Anal. Appl. 2022,6(4) :427–436. [5] LU class of oscillatory singular Integrals[J]. Inter. J. Appl. Math. Sci, 2022,2(1): 4764. [6] HU Guoen, LU Shanzhen, YANG of rough singular integral operators on homogeneous Herz spaces[J].J. Austral. Math. Soc. (Series A) 1999,66(2): 201223. [7] CHEN Jiecheng, JIA Houyu, JIANG Liya. Boundedness of rough oscillatory singular integral on Triebel–Lizorkin spaces[J]. J. Math. Anal. Appl. 2022,306(2):385 397. [8] SUN Yanling, JIANG Yinsheng. Rough singular integrals on Herztype TriebelLizorkin space and Herztype Besov space[J]. Journal of Xinjiang university (Natural Science Edition).2022,28(1):4246. [9] Coifman, R,Rochberg, R,Weiss, G. Factorization theorems for Hardy spaces in several variable. ,103:611635. [10] Janson S. Mean oscillation and mutators of singular integral operators[J]. ,16(2):263 一 270. [11] Paluszynski of the Besov spaces via mutator operator of Coifman,Rochberg and Weiss[J].Indiana ,44(1):117. [12] Coifman R. And Meyer dela des operateurs pseudodifferetiles[J]. ,57:1185. [13] Alvarez J. Bagby R. Kurtz D. And Prez estimates for mutators of linear operators[J].Studia ,104:195209. [14] Hu G, Lpboundedness for the mutators of a homgeneous singular operator [J].Studia ,154(01):1327. [15] Hern225。ndez E. Yang of Herz spaces and ,205(1):6987. [16] GarciaCuerva, de Francia, Norm inequalities and related ,Princeton NJ,1985. [17] Chen,Y. Ding,Y. Lp bounds for the mutator of parabolic singular integral with rough ,27:313334. [18] Chen,Y. Ding,Y. Rough singular integrals on TriebelLizorkin space and Besov ,347： 493501. Boundedness of Oscillatory Singular Integrals on Herztype Spaces YU Hubo, ZHAO Kai, JIANG Nuo, XI Fang, ZHANG Hongjun (College of Mathematics, Qingdao University, Qingdao 266071, China) Abstract: The boundedness of the oscillatory singular integral operator T is discussed. If )(log 1???? nSLL ,based on the boundedness ofT on pL spaces and Herztype spaces, the boundedness of the oscillatory singular integral operator T on the Herztype Besov spaces and the Herztype Triebel–Lizorkin spaces are obtained. Key words: Oscillatory singular integral。 Herz spaces。 Besov spaces。 Triebel–Lizorkin spaces。 boundedness
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