与F族相关的Fefferman-Stein不等式
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摘要
通过建立与F族相关的Calderon-Zygmund分解,以及应用R.Coifman和G.Wesis的证明方法,得到了与F族相关的good-λ不等式,证明了与F族相关的Fefferman-Stein不等式.
By establishing Calderon-Zygmund decomposition related to F family, and using the proof method of R.Coifman and G.Wesis, the good-λ inequality related to the F family is obtained, and the Fefferman-Stein inequality related to the F family is proved.
By establishing Calderon-Zygmund decomposition related to F family, and using the proof method of R.Coifman and G.Wesis, the good-λ inequality related to the F family is obtained, and the Fefferman-Stein inequality related to the F family is proved.
引文
[1]Caffarelli L A,Gutierrez C.Real analysis related to the Monge-Ampere equation[J].Transactions of the American Mathematical Society,1996,348(3):1 075-1 092.DOI:10.1090/S0002-9947-96-01473-0.
[2]Ding Y,Lin Q C.Hardy spaces associated to the sections[J].Tohoku Mathematical Journal,2005,57(2):147-170.DOI:10.2748/tmj/1119888333.
[3]Incognito A.Weak-type(1,1)inequality for the Monge-Ampere SIO’s[J].Journal of Fourier Analysis and Applications,2001,7(1):41-48.DOI:10.1007/s00041-001-0003-0.
[4]Coifman R R,Wesis G.Analysis Harmonique non-commutative surcertains espaces homogenes[M].New-York:Springer-Verlag,1971.
[5]周盼,周疆.强奇异积分算子在加权Amalgam空间上的有界性[J].云南大学学报:自然科学版,2017,39(6):930-936.Zhou P,Zhou J.Boundedness for strongly singular integral operator on weighted Amalgam space[J].Journal of Yunnan University:Natural Sciences Edition,2017,39(6):930-936.
[6]Caffarelli L A.Some regularity properties of solutions of Mongr-Ampere equation[J].Communications on Pure and Applied Mathematics,1991,44(8/9):965-969.DOI:10.1002/cpa.3160440809.
[7]Caffarelli L A.Boundary regularity of maps with convex potentials[J].Communications on Pure and Applied Mathematics,1992,45(9):1 141-1 151.DOI:10.1002/cpa.3160450905.
[8]Caffarelli L A,Gutierrez C E.Properties of the solutions of the linearized Monge-Ampere equation[J].American Journal of Mathematics,1997,119(2):423-465.DOI:10.1353/ajm.1997.0010.
[9]张霖,江寅生,曹勇辉.具有非光滑核的奇异积分交换子的加权估计[J].云南大学学报:自然科学版,2009,31(6):547-551.Zhang L,Jiang Y S,Cao Y H.Weighted estimates for Commutators of singular integral operators with non-smooth kernels[J].Journal of Yunnan University:Natural Sciences Edition,2009,31(6):547-551.
[10]Han Y,Lin Q C.Harmonic analysis and PDE’s[M].Cebu City:Matimyas Mathematics,2007:30.
[11]Meyer Y,Coifman R R.Wavelets:Calderon-Zygmund and mulitilinear operators[M].Cambridge:Cambridge University Press,1997.
[2]Ding Y,Lin Q C.Hardy spaces associated to the sections[J].Tohoku Mathematical Journal,2005,57(2):147-170.DOI:10.2748/tmj/1119888333.
[3]Incognito A.Weak-type(1,1)inequality for the Monge-Ampere SIO’s[J].Journal of Fourier Analysis and Applications,2001,7(1):41-48.DOI:10.1007/s00041-001-0003-0.
[4]Coifman R R,Wesis G.Analysis Harmonique non-commutative surcertains espaces homogenes[M].New-York:Springer-Verlag,1971.
[5]周盼,周疆.强奇异积分算子在加权Amalgam空间上的有界性[J].云南大学学报:自然科学版,2017,39(6):930-936.Zhou P,Zhou J.Boundedness for strongly singular integral operator on weighted Amalgam space[J].Journal of Yunnan University:Natural Sciences Edition,2017,39(6):930-936.
[6]Caffarelli L A.Some regularity properties of solutions of Mongr-Ampere equation[J].Communications on Pure and Applied Mathematics,1991,44(8/9):965-969.DOI:10.1002/cpa.3160440809.
[7]Caffarelli L A.Boundary regularity of maps with convex potentials[J].Communications on Pure and Applied Mathematics,1992,45(9):1 141-1 151.DOI:10.1002/cpa.3160450905.
[8]Caffarelli L A,Gutierrez C E.Properties of the solutions of the linearized Monge-Ampere equation[J].American Journal of Mathematics,1997,119(2):423-465.DOI:10.1353/ajm.1997.0010.
[9]张霖,江寅生,曹勇辉.具有非光滑核的奇异积分交换子的加权估计[J].云南大学学报:自然科学版,2009,31(6):547-551.Zhang L,Jiang Y S,Cao Y H.Weighted estimates for Commutators of singular integral operators with non-smooth kernels[J].Journal of Yunnan University:Natural Sciences Edition,2009,31(6):547-551.
[10]Han Y,Lin Q C.Harmonic analysis and PDE’s[M].Cebu City:Matimyas Mathematics,2007:30.
[11]Meyer Y,Coifman R R.Wavelets:Calderon-Zygmund and mulitilinear operators[M].Cambridge:Cambridge University Press,1997.