Lusin面积积分与局部Campanato函数生成的交换子在广义局部Morrey空间的有界性（英文）
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摘要
本文研究了Lusin面积积分及其交换子在广义局部Morrey空间的有界性.利用对Lusin面积积分μ_(?,S)的逐点估计及Hardy不等式,研究了Lusin面积积分μ_(?,S)在广义局部Morrey空间的有界性.类似地,还得到了Lusin面积积分μ_(?,S)与局部Campanato函数生成的交换子在广义局部Morrey空间的有界性,推广了已有的结果.
In the paper, the boundedness of the Lusin-area integral and its commutator on the generalized local Morrey spaces are established. Using the pointwise estimate of Lusin-area integral μ_(?,S) and Hardy inequality, we study the boundedness of the Lusin-area integral μ_(?,S) on the generalized local Morrey spaces, as well as the boundedness of the commutators generated byμ_(?,S) and local Campanato functions, which extend the previous results.
In the paper, the boundedness of the Lusin-area integral and its commutator on the generalized local Morrey spaces are established. Using the pointwise estimate of Lusin-area integral μ_(?,S) and Hardy inequality, we study the boundedness of the Lusin-area integral μ_(?,S) on the generalized local Morrey spaces, as well as the boundedness of the commutators generated byμ_(?,S) and local Campanato functions, which extend the previous results.
引文
[1]Chang S Y A,Wilson J M,Wolff T H.Some weighted norm inequalities concerning the Schrodinger operators[J].Comment.Math.Helv.,1985,60(1):217–246.
[2]Ding Y,Fan D S,Pan Y B.Weighted boundedness for a class of rough Marcinkiewicz integrals[J].India Univ.Math.J.,1999,48(3):1037–1055.
[3]Tao S P,Wei X M.Boundeness of Littlewood-Paley operators with rough kernels on the weighted Morrey spaces[J].J.Lanzhou Univ.,2013,49(3):400–404.
[4]Lin Y,Liu Z G,Mao D L,Sun Z K.Parameterized Littlewood-Paley operators and area integrals on weak Hardy spaces[J].Acta.Math.Sin.,2013,29(10):1857–1870.
[5]Ding Y,Lu S Z,Yabuta K.On commutators of Marcinkiewicz integrals with rough kernel[J].J.Math.Anal.Appl.,2002,275(1):60–68.
[6]Ding Y,Xue Q Y.Endpoint estimates for commutators of a class of Littlewood-Paley operators[J].Hokkaido.Math.J.,2007,36(2):245–282.
[7]Chen Y P,Ding Y,Wang X X.Commutators of Littlewood-Paley operators on the generalized Morrey space[J].J.Inequal.Appl.,2010(1),Artical ID:961502,20 pages.
[8]Chen Y P,Wang H.Compactness for the commutator of the parameterized area integral in the Morrey space[J].Math.Inequal.Appl.,2015,18(4):1261–1273.
[9]Morrey C B.On the solutions of quasi-linear elliptic partial differential equations[J].Trans.Amer.Math.Soc.,1938,43(1):126–166.
[10]Balakishiyev A S,Guliyev V S,Gurbuz F,Serbetci A.Sublinear operators with rough kernel generated by Calder′on-Zygmund operators and their commutators on generalized local Morrey spaces[J].J.Inequ.Appl.,2015,2015(1):1–18.
[11]Guliyev V S.Local generalized Morrey spaces and singular integrals with rough kernel[J].Azerb.J.Math.,2013,3(2):79–94.
[12]Guliyev V S.Generalized local Morrey spaces and fractional integral operators with rough kernel[J].J.Math.Sci.,2013,193(2):211–227.
[13]Zhang L,Zheng Q.Boundedness of commutators for singular integral operators with oscillating kernels on weighted Morrey spaces[J].J.Math.,2014,34(4):684–690.
[2]Ding Y,Fan D S,Pan Y B.Weighted boundedness for a class of rough Marcinkiewicz integrals[J].India Univ.Math.J.,1999,48(3):1037–1055.
[3]Tao S P,Wei X M.Boundeness of Littlewood-Paley operators with rough kernels on the weighted Morrey spaces[J].J.Lanzhou Univ.,2013,49(3):400–404.
[4]Lin Y,Liu Z G,Mao D L,Sun Z K.Parameterized Littlewood-Paley operators and area integrals on weak Hardy spaces[J].Acta.Math.Sin.,2013,29(10):1857–1870.
[5]Ding Y,Lu S Z,Yabuta K.On commutators of Marcinkiewicz integrals with rough kernel[J].J.Math.Anal.Appl.,2002,275(1):60–68.
[6]Ding Y,Xue Q Y.Endpoint estimates for commutators of a class of Littlewood-Paley operators[J].Hokkaido.Math.J.,2007,36(2):245–282.
[7]Chen Y P,Ding Y,Wang X X.Commutators of Littlewood-Paley operators on the generalized Morrey space[J].J.Inequal.Appl.,2010(1),Artical ID:961502,20 pages.
[8]Chen Y P,Wang H.Compactness for the commutator of the parameterized area integral in the Morrey space[J].Math.Inequal.Appl.,2015,18(4):1261–1273.
[9]Morrey C B.On the solutions of quasi-linear elliptic partial differential equations[J].Trans.Amer.Math.Soc.,1938,43(1):126–166.
[10]Balakishiyev A S,Guliyev V S,Gurbuz F,Serbetci A.Sublinear operators with rough kernel generated by Calder′on-Zygmund operators and their commutators on generalized local Morrey spaces[J].J.Inequ.Appl.,2015,2015(1):1–18.
[11]Guliyev V S.Local generalized Morrey spaces and singular integrals with rough kernel[J].Azerb.J.Math.,2013,3(2):79–94.
[12]Guliyev V S.Generalized local Morrey spaces and fractional integral operators with rough kernel[J].J.Math.Sci.,2013,193(2):211–227.
[13]Zhang L,Zheng Q.Boundedness of commutators for singular integral operators with oscillating kernels on weighted Morrey spaces[J].J.Math.,2014,34(4):684–690.