具有粗糙核的双线性分数次积分算子交换子在中心广义Morrey空间中的有界性
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摘要
研究了一类由λ-中心有界平均振荡空间中的函数生成的双线性分数次积分算子交换子,证明了双线性分数次积分算子的交换子在中心广义Morrey空间中的有界性.
The commutator of the bilinear fractional integral operators with a rough kernel generated by the functions belonged to the λ-central bounded mean oscillation space is studied and the boundedness of such operator on the center generalized Morrey space is proved.
The commutator of the bilinear fractional integral operators with a rough kernel generated by the functions belonged to the λ-central bounded mean oscillation space is studied and the boundedness of such operator on the center generalized Morrey space is proved.
引文
[1]Grafakos L.On multilinear fractional integrals[J].Studia Math,1992,102:49-56.
[2]Kenig C,Stein E.Multilinear estimates and fractional integration[J].Math Res Letters,1999,6:1-15.
[3]Chen Jiecheng,Fan Dashan.Some bilinear estimates[J].J Korean Math Soc,2009,46:609-620.
[4]Chen Jiecheng,Fan Dashan.Rough bilinear fractional integrals with variable kernels[J].Front Math China,2010,5:369-378.
[5]Chen Jiecheng,Fan Dashan.A bilinear fractional integral on compact Lie groups[J].Canad Math Bull,2011,54:207–216.
[6]Ding Yong,Lin Chincheng.Rough bilinear fractional integrals[J].Math Nachr,2002,246-247:47-52.
[7]Moen K.New weighted estimates for bilinear fractional integral operators[J].Trans Amer Math Soc,2014,366:627-646.
[8]Hoang C,Moen K.Weighted estimates for bilinear fractional integral and their commutators[J].Arxiv:1601.07590v1,to appear in Indiana Univ Math J.Online:http://www.iumj.indiana.edu/IUMJ/Preprints/6271.pdf.
[9]Wu Xiaomei,Chen Jiecheng.Boundedness of fractional integral operators onα-modulation spaces[J].Appl Math J Chinese Univ,Ser B,2014,29:339-351.
[10]Zhong Yong,Chen Jiecheng.Modulation space estimates for the fractional integral operators[J].Sci China Math,2011,54:1479-1489.
[11]Coifman R,Rochberg R,Weiss G.Factorization theorems for Hardy spaces in several variables[J].Ann Math,1976,103:611-635.
[12]Chanillo S.A note on commutators[J].Indina Univ Math J,1982,31:7-16.
[13]Morrey C B.On the solutions of quasi-linear elliptic partial differential equations[J].Trans Amer Math Soc,1938,43:126-166.
[14]Adams R.A note on Riesz Potentials[J].Duke Math J,1975,42:765-788.
[15]Chiarenza F,Frasca M.Morrey spaces and Hardy-Littlewood maximal function[J].Rend Math Appl,1987,7:273-279.
[16]Alvarez J,Lakey J,Guzm′an-Partida M.Spaces of boundedλ-central mean oscilation,Morrey spaces,andλ-central Carleson measures[J].Collect Math,2000,51:1-47.
[17]Guliyev V.Boundedness of the maximal,potential and singular operators in the generalized Morrey spaces[J].J Inequal Appl,2009,Article ID 503948:20 pages.
[18]Nakai E.Hardy-Littlewood maximal operator,singular integral operators and Riesz potentials on generalized Morrey spaces[J].Math Nachr,1994,166:95-103.
[19]Fan Yun,Gao Guilian.Some Estimates of Rough Bilinear Fractional Integral[J].J Func Spaces Appl,2012,406540:17 pages.
[20]Fu Zunwei,Lin Yan,Lu Shanzhen.λ-central BMO estimates for commutators of singular integrals with rough kernels[J].Acta Math Sinica,English Ser,2008,24:373-386.
[21]Guliyev V,Aliyev S,Shukurov P.Boundedness of sublinear operators and commutators on generalized Morrey spaces[J].Integral Equal Oper Theo,2011,71:327-335.
[22]Carro M,Pick L,Soria J et al.On embeddings between classical Lorentz spaces[J].Math Inequal Appl,2000,4:397–428.
[2]Kenig C,Stein E.Multilinear estimates and fractional integration[J].Math Res Letters,1999,6:1-15.
[3]Chen Jiecheng,Fan Dashan.Some bilinear estimates[J].J Korean Math Soc,2009,46:609-620.
[4]Chen Jiecheng,Fan Dashan.Rough bilinear fractional integrals with variable kernels[J].Front Math China,2010,5:369-378.
[5]Chen Jiecheng,Fan Dashan.A bilinear fractional integral on compact Lie groups[J].Canad Math Bull,2011,54:207–216.
[6]Ding Yong,Lin Chincheng.Rough bilinear fractional integrals[J].Math Nachr,2002,246-247:47-52.
[7]Moen K.New weighted estimates for bilinear fractional integral operators[J].Trans Amer Math Soc,2014,366:627-646.
[8]Hoang C,Moen K.Weighted estimates for bilinear fractional integral and their commutators[J].Arxiv:1601.07590v1,to appear in Indiana Univ Math J.Online:http://www.iumj.indiana.edu/IUMJ/Preprints/6271.pdf.
[9]Wu Xiaomei,Chen Jiecheng.Boundedness of fractional integral operators onα-modulation spaces[J].Appl Math J Chinese Univ,Ser B,2014,29:339-351.
[10]Zhong Yong,Chen Jiecheng.Modulation space estimates for the fractional integral operators[J].Sci China Math,2011,54:1479-1489.
[11]Coifman R,Rochberg R,Weiss G.Factorization theorems for Hardy spaces in several variables[J].Ann Math,1976,103:611-635.
[12]Chanillo S.A note on commutators[J].Indina Univ Math J,1982,31:7-16.
[13]Morrey C B.On the solutions of quasi-linear elliptic partial differential equations[J].Trans Amer Math Soc,1938,43:126-166.
[14]Adams R.A note on Riesz Potentials[J].Duke Math J,1975,42:765-788.
[15]Chiarenza F,Frasca M.Morrey spaces and Hardy-Littlewood maximal function[J].Rend Math Appl,1987,7:273-279.
[16]Alvarez J,Lakey J,Guzm′an-Partida M.Spaces of boundedλ-central mean oscilation,Morrey spaces,andλ-central Carleson measures[J].Collect Math,2000,51:1-47.
[17]Guliyev V.Boundedness of the maximal,potential and singular operators in the generalized Morrey spaces[J].J Inequal Appl,2009,Article ID 503948:20 pages.
[18]Nakai E.Hardy-Littlewood maximal operator,singular integral operators and Riesz potentials on generalized Morrey spaces[J].Math Nachr,1994,166:95-103.
[19]Fan Yun,Gao Guilian.Some Estimates of Rough Bilinear Fractional Integral[J].J Func Spaces Appl,2012,406540:17 pages.
[20]Fu Zunwei,Lin Yan,Lu Shanzhen.λ-central BMO estimates for commutators of singular integrals with rough kernels[J].Acta Math Sinica,English Ser,2008,24:373-386.
[21]Guliyev V,Aliyev S,Shukurov P.Boundedness of sublinear operators and commutators on generalized Morrey spaces[J].Integral Equal Oper Theo,2011,71:327-335.
[22]Carro M,Pick L,Soria J et al.On embeddings between classical Lorentz spaces[J].Math Inequal Appl,2000,4:397–428.