It is shown that the maximal singular integral operator with kernels satisfying Ho rmander＇s condition is of weak type （1,1） and L^p （1〈p〈∞） bounded without assuming that the underlying measure p is doubling. ...It is shown that the maximal singular integral operator with kernels satisfying Ho rmander＇s condition is of weak type （1,1） and L^p （1〈p〈∞） bounded without assuming that the underlying measure p is doubling. Under stronger smoothness conditions,such estimates can be obtained by using a Cotlar＇s inequality. This inequality is not applicable here and it is noticeable that the Cotlar＇s inequality maybe fails under Hormander＇s condition.展开更多
In this paper,we systematically study several classes of maximal singular integrals and maximal functions with rough kernels in Fβ(S^n-1),a topic that relates to the Grafakos-Stefanov class.The boundedness and contin...In this paper,we systematically study several classes of maximal singular integrals and maximal functions with rough kernels in Fβ(S^n-1),a topic that relates to the Grafakos-Stefanov class.The boundedness and continuity of these operators on Triebel-Lizorkin spaces and Besov spaces are discussed.展开更多
The authors study the singular integrals under the Hormander condition and the measure not satisfying the doubling condition. At first, if the corresponding singular integral is bounded from L^2 to itself, it is prove...The authors study the singular integrals under the Hormander condition and the measure not satisfying the doubling condition. At first, if the corresponding singular integral is bounded from L^2 to itself, it is proved that the maximal singular integral is bounded from L^∞ to RBMO except that it is infinite μ-a.e. on R^d. A sufficient condition and a necessary condition such that the maximal singular integral is bounded from L^2 to itself are also obtained. There is a small gap between the two conditions.展开更多
Given a positive Radon measure μ on R^d satisfying the linear growth condition μ（B（x,r））≤C0r^n,x∈R^d,r〉0,（1） where n is a fixed number and O〈n≤d. When d-1〈n,it is proved that if Tt,N1=0,then the correspo...Given a positive Radon measure μ on R^d satisfying the linear growth condition μ（B（x,r））≤C0r^n,x∈R^d,r〉0,（1） where n is a fixed number and O〈n≤d. When d-1〈n,it is proved that if Tt,N1=0,then the corresponding maximal Calderon-Zygmund singular integral is bounded from RBMO to itself only except that it is infinite μ-a. e. on R^d.展开更多
A weak type endpoint estimate for the maximal multilinear singular integral operator TAf（x）=supε〉0｜∫｜x-y｜〉εΩ（x-y）/｜x-y｜^n＋1（A（x）-A（y）-VA（y）（x-y））f（y）dy｜ is established, where Ω is homogen...A weak type endpoint estimate for the maximal multilinear singular integral operator TAf（x）=supε〉0｜∫｜x-y｜〉εΩ（x-y）/｜x-y｜^n＋1（A（x）-A（y）-VA（y）（x-y））f（y）dy｜ is established, where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one, and A has derivatives of order one in BMO（R^n）. A regularity condition on Ω which implies an LlogL type estimate of TA is given.展开更多
Le be a nonnegative Radon measure on Rd which satisfies the growth condition （B（x, r）） Cotfor all x E Rd and r 〉 O, where Co is a fixed constant and 0 〈 n d. The purpose of this paper is to establish the boun...Le be a nonnegative Radon measure on Rd which satisfies the growth condition （B（x, r）） Cotfor all x E Rd and r 〉 O, where Co is a fixed constant and 0 〈 n d. The purpose of this paper is to establish the boundedness of the Marcinkiewicz integrals from LP（u） to LP（u）, where u is a weight function of Muckenhoupt type associated with ~.展开更多
The main purpose of this paper is to investigate the properties of the higher order commutators of maximal Calderón-Zygmund operators with Dini-type kernels.Two weighted estimates have been established for these ...The main purpose of this paper is to investigate the properties of the higher order commutators of maximal Calderón-Zygmund operators with Dini-type kernels.Two weighted estimates have been established for these commutators.Similar results have also been extended to multilinear setting.展开更多
We introduce a class of singular integral operators on product domains along twisted surfaces.We prove that the operators are bounded on L^(p) provided that the kernels satisfy weak conditions.
基金Supported by the Science Foundation of the Education Department of Zhejiang Province （20050316）.
文摘It is shown that the maximal singular integral operator with kernels satisfying Ho rmander＇s condition is of weak type （1,1） and L^p （1〈p〈∞） bounded without assuming that the underlying measure p is doubling. Under stronger smoothness conditions,such estimates can be obtained by using a Cotlar＇s inequality. This inequality is not applicable here and it is noticeable that the Cotlar＇s inequality maybe fails under Hormander＇s condition.
基金supported by National Natural Science Foundation of China(Grant No.11701333)Support Program for Outstanding Young Scientific and Technological Top-Notch Talents of College of Mathematics and Systems Science(Grant No.Sxy2016K01)+3 种基金supported by National Natural Science Foundation of China(Grant Nos.11471041 and 11671039)National Natural Science Foundation of China-Deutsche Forschungsgemeinschaft(Grant No.11761131002)supported by Grant-in-Aid for Scientific Research(C)(Grant No.15K04942)Japan Society for the Promotion of Science。
文摘In this paper,we systematically study several classes of maximal singular integrals and maximal functions with rough kernels in Fβ(S^n-1),a topic that relates to the Grafakos-Stefanov class.The boundedness and continuity of these operators on Triebel-Lizorkin spaces and Besov spaces are discussed.
基金Project supported by the 973 Project of the Ministry of Science and Technology of China (No.G1999 075105) the National Natural Science Foundation of China (No. 10271107) the Research Fund for the Doctoral Program of Higher Education (No.20030335019) the Zhejiang Provincial Natural Science Foundation of China (No.RC97017).
文摘The authors study the singular integrals under the Hormander condition and the measure not satisfying the doubling condition. At first, if the corresponding singular integral is bounded from L^2 to itself, it is proved that the maximal singular integral is bounded from L^∞ to RBMO except that it is infinite μ-a.e. on R^d. A sufficient condition and a necessary condition such that the maximal singular integral is bounded from L^2 to itself are also obtained. There is a small gap between the two conditions.
文摘Given a positive Radon measure μ on R^d satisfying the linear growth condition μ（B（x,r））≤C0r^n,x∈R^d,r〉0,（1） where n is a fixed number and O〈n≤d. When d-1〈n,it is proved that if Tt,N1=0,then the corresponding maximal Calderon-Zygmund singular integral is bounded from RBMO to itself only except that it is infinite μ-a. e. on R^d.
文摘A weak type endpoint estimate for the maximal multilinear singular integral operator TAf（x）=supε〉0｜∫｜x-y｜〉εΩ（x-y）/｜x-y｜^n＋1（A（x）-A（y）-VA（y）（x-y））f（y）dy｜ is established, where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one, and A has derivatives of order one in BMO（R^n）. A regularity condition on Ω which implies an LlogL type estimate of TA is given.
基金Supported by the National Natural Science Foundation of China (Grant No. 10861010)
文摘Le be a nonnegative Radon measure on Rd which satisfies the growth condition （B（x, r）） Cotfor all x E Rd and r 〉 O, where Co is a fixed constant and 0 〈 n d. The purpose of this paper is to establish the boundedness of the Marcinkiewicz integrals from LP（u） to LP（u）, where u is a weight function of Muckenhoupt type associated with ~.
文摘The main purpose of this paper is to investigate the properties of the higher order commutators of maximal Calderón-Zygmund operators with Dini-type kernels.Two weighted estimates have been established for these commutators.Similar results have also been extended to multilinear setting.
文摘We introduce a class of singular integral operators on product domains along twisted surfaces.We prove that the operators are bounded on L^(p) provided that the kernels satisfy weak conditions.
