Acta mathematica scientia,Series A ›› 2018, Vol. 38 ›› Issue (4): 716-727.
Previous Articles Next Articles
Wang Liwei1, Shu Lisheng2
Received:
2017-08-09
Revised:
2017-12-18
Online:
2018-08-26
Published:
2018-08-26
Supported by:
CLC Number:
Wang Liwei, Shu Lisheng. Boundedness of the Intrinsic Square Function on Variable Exponent Herz and Herz-Hardy Spaces[J].Acta mathematica scientia,Series A, 2018, 38(4): 716-727.
[1] | Wilson M. The intrinsic square function. Rev Mat Iberoam, 2007, 23:771-791 |
[2] | Fefferman C, Stein E M. Some maximal inequalities. Amer J Math, 1971, 93:107-115 |
[3] | Liang Y, Yang D. Intrinsic square function characterizations of Musielak-Orlicz Hardy spaces. Trans Amer Math Soc, 2015, 367:3225-3256 |
[4] | Zhuo C, Yang D, Liang Y. Intrinsic square function characterizations of Hardy spaces with variable exponents. Bull Malays Math Sci Soc, 2016, 39:1541-1577 |
[5] | Ho K P. Intrinsic square functions on Morrey and Block spaces with variable exponents. Bull Malays Math Sci Soc, 2017, 40:995-1010 |
[6] | Wilson M. Weighted Littlewood-Paley Theory and Exponential-Square Integrability. Berlin:SpringerVerlag, 2007 |
[7] | Kováčik O, Rákosník J. On spaces Lp(x) and Wk,p(x). Czechoslovak Math J, 1991, 41:592-618 |
[8] | Cruz-Uribe D, Fiorenza A, Neugebauer C. The maximal function on variable Lp spaces. Ann Acad Sci Fenn Math, 2003, 28:223-238 |
[9] | Diening L. Maximal function on generalized Lebesgue spaces Lp(·). Math Inequal Appl, 2004, 7:245-253 |
[10] | Harjulehto P, Hästö P, Lê Ú V, Nuortio M. Overview of differential equations with non-standard growth. Nonlinear Anal, 2010, 72:4551-4574 |
[11] | Nekvinda A. Hardy-littlewood maximal operator in Lp(x)(Rn). Math Inequal Appl, 2004, 7:255-265 |
[12] | Tan J, Liu Z, Zhao J. On some multilinear commutators in variable Lebesgue spaces. J Math Inequal, 2017, 11:715-734 |
[13] | Zhang P, Wu J. Commutators for the maximal function on Lebesgue spaces with variable exponent. Math Inequal Appl, 2014, 17:1375-1386 |
[14] | Almeida A, Drihem D. Maximal, potential and singular type operators on Herz spaces with variable exponents. J Math Anal Appl, 2012, 394:781-795 |
[15] | Dong B, Xu J. Variable Herz-type Hardy spaces and their applications. Anal Theory Appl, 2015, 31:321-353 |
[16] | Dong B, Xu J. New Herz type Besov and Triebel-Lizorkin spaces with variable exponents. J Funct Space Appl, 2012, Article ID:384593 |
[17] | Izuki M. Commutators of fractional integrals on Lebesgue and Herz spaces with variable exponent. Rend Circ Mat Palermo, 2010, 59:461-472 |
[18] | Lu Y, Zhu Y. Boundedness of multilinear Calderón-Zygmund singular operators on Morrey-Herz spaces with variable exponents. Acta Math Sin (Engl Ser), 2014, 30:1180-1194 |
[19] | Tao S, Wang L. Littlewood-Paley operators on Morrey spaces with variable exponent. The Scientific World Journal, 2014, Article ID:790671 |
[20] | Wang H, Liu Z. The Herz-type Hardy spaces with variable exponent and thier applications. Taiwanese J Math, 2012, 16:1363-1389 |
[21] | Yang D, Zhuo C, Yuan W. Besov-type spaces with variable smoothness and integrability. J Funct Anal, 2015, 269:1840-1898 |
[22] | Cruz-uribe D, Fiorenza A. Variable Lebesgue Spaces:Foundations and Harmonic Analysis, Applied and Numerical Harmonic Analysis. Boston:Birkhäuser Basel, 2013 |
[23] | Diening L, Harjulehto P, Hästö P, R·užička M. Lebesgue and Sobolev Spaces with Variable Exponents. Heidelberg:Springer, 2011 |
[24] | Wang H. The boundedness of intrinsic square functions on the weighted Herz spaces. J Funct Spaces, 2014, Article ID:274521 |
[25] | Wang H. Some estimates of intrinsic square functions on the weighted Herz-type Hardy spaces. J Inequal Appl, 2015, 2015(1):62 |
[26] | Diening L. Maximal function on Musielak-Orlicz spaces and generalized Lebesgue spaces. Bull Sci Math, 2005, 129:657-700 |
[27] | Fefferman C, Stein E M. Hp spaces of several variables. Acta Math, 1972, 129:137-193 |
[28] | Lu S, Yang D, Hu G. Herz Type Spaces and Their Applications. Beijing:Science Press, 2008 |
[29] | Nakai E, Sawano Y. Hardy spaces with variable exponents and generalized Campanato spaces. J Funct Anal, 2012, 262:3665-3748 |
[30] | Yan X, Yang D, Yuan W, Zhuo C. Variable weak Hardy spaces and their applications. J Funct Anal, 2016, 271:2822-2887 |
[1] | Fang Jingxuan, Zhao Jiman. Variable Homogeneous Besov and Triebel-Lizorkin Spaces on Stratified Groups [J]. Acta mathematica scientia,Series A, 2018, 38(1): 34-45. |
[2] | Wu Ruimin, Jiang Yinsheng, Wang Lihong, Gao Jinling. Weighted Estimates for Parametric Marcinkiewicz Integrals and Its Commutators [J]. Acta mathematica scientia,Series A, 2017, 37(1): 26-37. |
[3] | Huang Wenli, Tao Xiangxing. Weighted Estimates on the Neumann Problem for L2 for Schrödinger Equations in Lipschitz Domains [J]. Acta mathematica scientia,Series A, 2016, 36(6): 1165-1185. |
[4] | Chen Dongxiang, Chen Xuemei. Lp Boundedness for Some Commutators Related to Schrödinger Operator [J]. Acta mathematica scientia,Series A, 2016, 36(5): 832-847. |
[5] | Xu Meiyu, Lu Dayong. Frame Properties of Wave Packet Systems in Sobolev Spaces Hs(Rd) [J]. Acta mathematica scientia,Series A, 2016, 36(5): 848-860. |
[6] | Chen Dongxiang, Zhou Wenjuan, Fang Yuda. The Boundedness of the Commutator of Riesz Potential Associated with Schrödinger Operators [J]. Acta mathematica scientia,Series A, 2016, 36(1): 117-129. |
[7] | Wang Songbai, Pan Jibing, Jiang Yinsheng. Necessary and Sufficient Conditions for Boundedness of Commutators of Multilinear Fractional Integral Operators [J]. Acta mathematica scientia,Series A, 2015, 35(6): 1106-1114. |
[8] | SHU Lisheng. Boundedness of the intrinsic square function on variable Herz and Herz-Hardy spaces [J]. Acta mathematica scientia,Series A, , (): 0-0. |
Viewed | ||||||||||||||||||||||||||||||||||||||||||||||||||
Full text 125
|
|
|||||||||||||||||||||||||||||||||||||||||||||||||
Abstract 99
|
|
|||||||||||||||||||||||||||||||||||||||||||||||||
Cited |
|
|||||||||||||||||||||||||||||||||||||||||||||||||
Shared | ||||||||||||||||||||||||||||||||||||||||||||||||||
Discussed |
|