|
|
- 2016
Littlewood-Paley算子及其交换子在变指数Herz空间上的有界性
|
Abstract:
摘要： 研究了Littlewood-Paley积分算子(包括Lusin面积积分函数,Littlewood-Paley g函数和 g*λ函数)及其与BMO函数生成的高阶交换子在具有两个变指数p(·),α(·)的Herz空间上的有界性, 这里p(·),α(·)均满足一定的连续性条件。
Abstract: The main result in the paper is the boundedness of the Littlewood-Paley integral operators(include Lusin area integral function, Littlewood-Paley g and g*λ)and its higher order commutators generated by BMO fucntions on the Herz spaces with two variable exponents p(·),α(·), where p(·),α(·) satisfies some continuous condition
| [1] | LU Shanzhen, YANG Dachun. The central BMO spaces and Littlewood-Paley operators[J]. Approx Theory Appl, 1995, 11(3):72-94. |
| [2] | LI Xinwei, YANG Dachun. Boundedness of some sublinear operators on Herz spaces[J]. Illinois Journal of Mathematics, 1996, 40(3):484-501. |
| [3] | LIU Lanzhe, LU Shanzhen, XU Jingshi. Boundedness of commutators of Littlewood-Paley operators[J]. Andvances in Mathematics, 2003, 32(4):473-480. |
| [4] | 陈杰诚,丁勇,范大山.带变量核的Littlewood-Paley算子[J]. 中国科学:A辑数学, 2006, 36(1):38-51. CHEN Jiecheng, DING Yong, FAN Dashan.Littlewood-Paley operator with variable kernel[J].Science in China: Series A Mathematics, 2006, 36(1):38-51. |
| [5] | 陈艳萍,丁勇.广义Morrey空间上带变量核的的Littlewood-Paley算子[J]. 数学物理学报, 2009, 29A(3):630-642. CHEN Yanping, DING Yong. Littlewood-Paley operator with variable kernel on generalized Morrey spaces[J]. Acta Mathematica: Scientia-Chinese series, 2009, 29A(3):630-642. |
| [6] | XUE Qingying, DING Yong. Weighted estimates for multilinear commutators of the Littlewood-Paley operators[J].Science in China: Series A Mathematics, 2009, 52(9):1849-1868. |
| [7] | Kovácik O, Rákosník J. On spaces <i>L<sup>p(x)</sup></i> and <i>W<sup>k,p(x)</sup></i>[J]. Czechoslovak Math J, 1991, 41(4):592-618. |
| [8] | CRUZ-URIBE SFO D, FIORENZA A, MARTELL M J, et al. The boundedness of classical operators on variable <i>L<sup>p</sup></i> spaces[J]. Ann Acad Sci Fenn Math, 2006, 31(1):239-264. |
| [9] | WANG Hongbin, FU Zunwei, LIU Zongguang. Higher-order commutators of Marcinkiewicz integrals on variable Lebesgue spaces[J]. Acta Math Sci, 2012, 32A(6):1092-1101. |
| [10] | IZUKI M. Herz and amalgam spaces with variable exponent, the Haar wavelets and greediness of the wavelet system[J]. East Journal on Approximations, 2009, 15(1):87-109. |
| [11] | IZUKI M. Commutators of fractional integrals on Lebesgue and Herz spaces with variable exponent[J]. Rend Circ Mat Palermo, 2010, 59(3):461-472. |
| [12] | ALMEIDA A, DRIHEM D. Maximal, potential and singular type operators on Herz spaces with variable exponents[J]. J Math Anal Appl, 2012, 394(2):781-795. |
| [13] | LU Yan, ZHU Yueping. Boundedness of multilinear Calderón-Zygmund singular operators on Morrey-Herz spaces with variable exponents[J]. Acta Mathematica Sinica: English Series, 2014, 30(7):1180-1194. |
| [14] | WANG Lijuan, TAO Shuangping. Boundedness of Littlewood-Paley operators and their commutators on Herz-Morrey spaces with exponent[J]. Journal of Inequalities and Applications, 2014, 2014(1):227. |
| [15] | DONG Baohua, XU Jingshi. New Herz type Besov and Triebel-Lizorkin spaces with variable exponents [J]. J of Function Spaces and Applications, 2012, 27. pages, id: 384593. |
| [16] | IZUKI M. Vector-valued inequalities on Herz spaces and characterizations of Herz-Sobolev spaces with variable exponent[J]. Glasnik Mat, 2010, 45(2):475-503. |
| [17] | WANG Liwei. Marcinkiewicz integral operators and commutators on Herz spaces with variable exponents[J]. J Function Space and Applications, 2014, id:430635. |
