加权变指数Herz乘积空间上的多线性奇异积分算子
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摘要
根据加权变指数Lebesgue空间和Herz空间的定义和性质,利用变指标特征,应用H9lder不等式等估计,证明多线性Calderón-Zygmund算子在加权变指数Lebesgue乘积空间上的有界性,进而证明该算子在加权变指数Herz乘积空间上有界.
According to the definitions and properties of the weighted Lebesgue spaces and Herz spaces with variable exponent,using the property of variable index,and by the estimates of the Hlder inequalities,we proved the boundedness of the multilinear Calderón-Zygmund operators on the product of weighted Lebesgue spaces with variable exponent,and then proved the operators were bounded on the product of weighted Herz spaces with variable exponent.
According to the definitions and properties of the weighted Lebesgue spaces and Herz spaces with variable exponent,using the property of variable index,and by the estimates of the Hlder inequalities,we proved the boundedness of the multilinear Calderón-Zygmund operators on the product of weighted Lebesgue spaces with variable exponent,and then proved the operators were bounded on the product of weighted Herz spaces with variable exponent.
引文
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[2]陶双平,王萍.Calderón-Zygmund算子与交换子在非齐度量测度空间上Morrey空间中的有界性[J].吉林大学学报(理学版),2015,53(6):1073-1080.(TAO Shuangping,WANG Ping.Boundedness of Calderón-Zygmund Operators and Commutators on Morrey Spaces Associated with Non-Homogenous Metric Measure Spaces[J].Journal of Jilin University(Science Edition),2015,53(6):1073-1080.)
[3]陶双平,杨沿奇.变量核奇异积分与分数次微分的加权Morrey-Herz空间有界性[J].吉林大学学报(理学版),2016,54(4):677-684.(TAO Shuangping,YANG Yanqi.Boundedness of Weighted Morrey-Herz Spaces with Variable Kernel Singular Integrals and Fractional Differentiations[J].Journal of Jilin University(Science Edition),2016,54(4):677-684.)
[4]Coifman R R,Meyer Y.On Commutators of Singular Integrals and Bilinear Singular Integrals[J].Trans Amer Math Soc,1975,212:315-331.
[5]Grafakos L,Torres R H.Multilinear Calderón-Zygmund Theory[J].Adv Math,2002,165(1):124-164.
[6]Grafakos L,Torres R H.On Multilinear Singular Integrals of Calderón-Zygmund Type[J].Pub Mat,2002,46(Suppl):57-91.
[7]Grafakos L,Kalton N.Multilinear Calderón-Zygmund Operators on Hardy Spaces[J].Collect Math,2001,52(2):169-179.
[8]周疆,江寅生,马柏林,等.多线性Calderón-Zygmund在Herz-Morrey空间上的有界性[J].兰州大学学报(自然科学版),2009,45(1):83-87.(ZHOU Jiang,JIANG Yinsheng,MA Bolin,et al.Boundedness of Multilinear Calderón-Zygmund Singular Integrals Operators on Herz-Morrey Spaces[J].Journal of Lanzhou University(Nature Science),2009,45(1):83-87.)
[9]胡国恩.多线性Calderón-Zygmund算子的加权估计[J].中国科学(A辑:数学),2009,39(12):1421-1434.(HU Guo’en.Weighted Norm Inequalities for the Multilinear Calderón-Zygmund Operators[J].Science in China(Series A:Mathematics),2009,39(12):1421-1434.)
[10]Orlicz W.ber Konjugierte Exponentenfolgen[J].Studia Math,1931,3(1):200-212.
[11]Kovacik O,Rakosnik J.On Spaces Lp(x)and Wk,p(x)[J].Czechoslovak Math J,1991,41(4):592-618.
[12]WANG Lijuan,TAO Shuangping.Parameterized Littlewood-Paley Operators and Their Commutators on Herz Spaces with Variable Exponent[J].Turkish J Math,2016,40(1):122-145.
[13]HUANG Aiwu,XU Jingshi.Multilinear Singular Integrals and Commutators in Variable Exponent Lebesgue Spaces[J].Appl Math J Chinese Univ(Ser B),2010,25(1):69-77.
[14]LU Yan,ZHU Yueping.Boundedness of Multilinear Calderón-Zygmund Singular Operators on Morrey-Herz Spaces with Variable Exponents[J].Acta Math Sin(Eng Ser),2014,30(7):1180-1194.
[15]ZHANG Meirong,ZHAO Kai.Multilinear Singular Integral on Herz-Hardy Spaces with Variable Exponent[J].Math Appl,2017,30(1):98-104.
[16]Izuki M,Noi T.An Intrinsic Square Function on Weighted Herz Spaces with Variable Exponent[J/OL].2016-06-06.http://arxiv.org/abs/1606.01019.
[17]Cruz-Uribe D,WANG Li’an.Daniel Extrapolation and Weighted Norm Inequalities in the Variable Lebesgue Spaces[J].Trans Amer Math Soc,2017,369(2):1205-1235.
[18]Pérez C,Trujillo-GonzAlez R.Sharp Weighted Estimates for Vector-Valued Singular Integral Operators and Commutators[J].Tohoku Math J,2003,55(1):109-129.
[19]Pérez C,Torres R H.Sharp Maximal Function Estimates for Multilinear Singular Integrals[M]//Holyoke M,ed.Harmonic Analysis.Providence,RI:Amer Math Soc,2003:323-331.