带变量核的变指数分数次积分算子（英文）
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摘要
本文利用变指标Hardy空间的原子分解,应用经典不等式和变指数的性质,证明了带变量核的变指数分数次积分算子从变指标Hardy空间到变指标Lebesgue空间的有界性.
In this paper, by the atomic decomposition of the Hardy spaces with variable exponents, using the estimates of classical inequality and the properties of the variable exponents, we proved that the fractional integral operators with variable kernels associated to variable exponents are bounded from the Hardy spaces to Lebesgue spaces with variable exponents.
In this paper, by the atomic decomposition of the Hardy spaces with variable exponents, using the estimates of classical inequality and the properties of the variable exponents, we proved that the fractional integral operators with variable kernels associated to variable exponents are bounded from the Hardy spaces to Lebesgue spaces with variable exponents.
引文
[1]CALDER′ON A P,ZYGMUND A.On a problem of Mihlin[J].Trans.Amer.Math.Soc.,1955,78(1):209-224.
[2]MUCKENHOUPT B,WHEEDEN R L.Weighted norm inequalities for singular and fractional integrals[J].Trans.Amer.Math.Soc.,1971,161:249-258.
[3]DING Yong,LIN Chincheng.On Marcinkiewicz integral with variable kernels[J].Indiana Univ.Math.J.,2004,53(3):805-822.
[4]许永华,束立生.带变量核的分数次积分算子在Hardy空间上的有界性[J].纯粹数学与应用数学,2011,27(2):199-203.
[5]HE Suixin,ZHOU Jian.Necessary and sufficient conditions for boundedness of commutators of bilinear fractional integral operators on Morrey spaces[J].J.Math.Res.Appl.,2016,36(6):711-717.
[6]NAKAI E,SAWANO Y.Hardy spaces with variable exponents and generalized Campanato spaces[J].J.Funct.Anal.,2012,262(9):3665-3748.
[7]徐景实.变指标函数空间的进展[J].数学进展,2015,44(1):1-22.
[8]CHENG Xingxing,SHU Lisheng.Boundedness for some Hardy type operators on Herz-Morrey spaces with variable exponent[J].J.Anhui Normal Univ.,2015,38(1):19-24.
[9]檀健,刘宗光.齐次分数次积分算子在变指标函数空间上的有界性[J].数学学报(中文版),2015,58(2):309-320.
[10]CRUZ-URIBE D,FIORENZA A.Variable Lebesgue Spaces:Foundations and Harmonic Analysis[M].Basel:Birkh¨auser,2013.
[11]CRUZ-URIBE D,FIORENZA A,NEUGEBAUER C J.The maximal function on variable Lpspaces[J].Ann.Acad.Sci.Fen.Math.,2003,28:223-238.
[12]DIENING L,HARJULEHTO P,HASTO P et al.Lebesgue and Sobolev Spaces with Variable Exponents[M].New York:Springer,2010.
[13]IZUKI M.Boundedness of commutators on Herz spaces with variable exponent[J].Rendiconti del Circolo Matematico di Palermo,2010,59(2):199-213.
[14]姚俊卿,赵凯.变指数Herz-Morrey空间上的分数次积分交换子[J].山东大学学报(理学版),2017,52(11):100-105.
[15]ALMEIDA A,HASANOV J,SAMKO S.Maximal and potential operators in variable exponent Morrey spaces[J].Geo.Math.J.,2008,15(2):195-208.
[16]TANG Canqin,WU Qing,XU Jingshi.Estimates of fractional integral operators on variable exponent Lebesgue spaces[J].J.Func.Spaces,2016,Article ID 2438157,7 pages.
[2]MUCKENHOUPT B,WHEEDEN R L.Weighted norm inequalities for singular and fractional integrals[J].Trans.Amer.Math.Soc.,1971,161:249-258.
[3]DING Yong,LIN Chincheng.On Marcinkiewicz integral with variable kernels[J].Indiana Univ.Math.J.,2004,53(3):805-822.
[4]许永华,束立生.带变量核的分数次积分算子在Hardy空间上的有界性[J].纯粹数学与应用数学,2011,27(2):199-203.
[5]HE Suixin,ZHOU Jian.Necessary and sufficient conditions for boundedness of commutators of bilinear fractional integral operators on Morrey spaces[J].J.Math.Res.Appl.,2016,36(6):711-717.
[6]NAKAI E,SAWANO Y.Hardy spaces with variable exponents and generalized Campanato spaces[J].J.Funct.Anal.,2012,262(9):3665-3748.
[7]徐景实.变指标函数空间的进展[J].数学进展,2015,44(1):1-22.
[8]CHENG Xingxing,SHU Lisheng.Boundedness for some Hardy type operators on Herz-Morrey spaces with variable exponent[J].J.Anhui Normal Univ.,2015,38(1):19-24.
[9]檀健,刘宗光.齐次分数次积分算子在变指标函数空间上的有界性[J].数学学报(中文版),2015,58(2):309-320.
[10]CRUZ-URIBE D,FIORENZA A.Variable Lebesgue Spaces:Foundations and Harmonic Analysis[M].Basel:Birkh¨auser,2013.
[11]CRUZ-URIBE D,FIORENZA A,NEUGEBAUER C J.The maximal function on variable Lpspaces[J].Ann.Acad.Sci.Fen.Math.,2003,28:223-238.
[12]DIENING L,HARJULEHTO P,HASTO P et al.Lebesgue and Sobolev Spaces with Variable Exponents[M].New York:Springer,2010.
[13]IZUKI M.Boundedness of commutators on Herz spaces with variable exponent[J].Rendiconti del Circolo Matematico di Palermo,2010,59(2):199-213.
[14]姚俊卿,赵凯.变指数Herz-Morrey空间上的分数次积分交换子[J].山东大学学报(理学版),2017,52(11):100-105.
[15]ALMEIDA A,HASANOV J,SAMKO S.Maximal and potential operators in variable exponent Morrey spaces[J].Geo.Math.J.,2008,15(2):195-208.
[16]TANG Canqin,WU Qing,XU Jingshi.Estimates of fractional integral operators on variable exponent Lebesgue spaces[J].J.Func.Spaces,2016,Article ID 2438157,7 pages.