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Boundedness for commutators of fractional Hardy operators on Herz spaces

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Progress in Natural Science:Materials International 2007年第1期17卷 20-25页

作者： FU Zunwei, LIU Zongguang and LU Shanzhen ( School of Mathematical Sciences, Beijing normal university, Beijing 100875, china department of mathematics, linyi normal university, linyi 276005, china department of mathematics, china university of Mining and Technology, Beijing 100083, china) [a]School of Mathematical Sciences Beijing Normal University Beijing China [b]Departhent of mathematics Linyi Normal University Linyi China [c]Departhent of mathematics China University of Mining and Technology Beijing China

Some boundedness results are established for commutators generated by classical fractional Hardy operators and one-sided CMO functions on the homogeneous Herz spaces, which extends some known results.

关键词： fractional Hardy operator Hardy’s integral inequality commutator one-sided CMO function homogeneous Herz space.

Characterization for commutators of n-dimensional fractional Hardy operators

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Science china mathematics 2007年第10期50卷 1418-1426页

作者： Zun-wei FU~(1,2) Zong-guang LIU~3 Shan-zhen LU~(1+) Hong-bin WANG~3 ~1 School of Mathematical Sciences,Beijing normal university,Beijing 100875,china ~2 department of mathematics,linyi normal university,linyi 276005,china ~3 department of mathematics,china university of Mining and Technology (Beijing),Beijing 100083,china 1. School of Mathematical Sciences Beijing Normal University Beijing 100875 China 2. department of mathematics Linyi Normal University Linyi 276005 China 3. department of mathematics China University of Mining and Technology (Beijing) Beijing 100083 China

In this paper,it was proved that the commutator H_(β,b)generated by an n-dimensional fractional Hardy operator and a locally integrable function b is bounded from L^(p1)(R^n)to L^(p2)(R^n)if and only if b is a CMO(R^... 详细信息

关键词： n-dimensional fractional Hardy operator, commutator, C(M)O function, homogeneous Herz space

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Hardy空间上的非游荡复合算子

山东大学学报（理学版） 2009年第3期44卷 81-83页

作者：张蕾临沂师范学院数学系山东临沂276005

非游荡算子是一种新型的混沌算子,证明在经典的Hardy空间(H2)上,由双曲线性映射诱导的复合算子是非游荡的,而且进一步证明该结论在更一般空间Hp和Bp上成立。

关键词：复合算子非游荡算子 Hardy空间 Bergman空间

DEGENERATED HOMOCLINIC BIFURCATIONS WITH HIGHER DIMENSIONS

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Chinese Annals of mathematics,Series B 2000年第2期21卷 201-210页

作者： JINYINLAI ZHUDEMINC departmentofmathematics EastChinaNormalUniversityShanghai200062China. departmentofmathematics LinyiTeacherCollegeLinyi276005ShandongChina.

The degenerated homoclinic bifurcation for high dimensional system is considered. The existence, uniqueness, and incoexistence of the 1-homclinic orbit and 1-periodic orbit near　Г are studied under the nonresonant c... 详细信息

关键词： Local coordinates Poincare map Homoclinic orbit Periodic orbit 2-fold periodic orbit Resonant condition

EQUIVALENT CONDITIONS FOR THE FINITENESS OF GAUGE

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Systems Science and Mathematical Sciences 1997年第4期10卷 299-308页

作者： YIN Chuancun(department of mathematics, Qufu normal university, Shandong 273165, china)JIANG Zhaolin(department of mathematics, linyi Teacher,College, Shandong 276005, china)

Some equivalent conditions for the finiteness of gauge on a class of unboundeddomains in Rd are given.

关键词： Gauge additive functional Brownian motion.

Bifurcations of Rough Heteroclinic Loops with Three Saddle Points

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Acta Mathematica Sinica,English Series 2002年第1期18卷 199-208页

作者： JIN Yin Lai ZHU De Ming department of mathematics. linyi Teachers university. Shandong 276005. P. R. china department of mathematics. East china normal university. Shanghai 200062. P. R. china department of mathematics. East china normal university. Shanghai 200062. P. R. china department of mathematics Linyi Teachers' University Shandong P. R. China department of mathematics East China Normal University Shanghai P. R. China

In this paper, we study the bifurcation problems of rough heteroclinic loups cormecting threc saddle points for a higher-dimensional system. Under some transversal conditions and the nontwisted condition. the existence. uniqueness. nd incoexistencc of thc l-heteroclinic loop with threc or two saddle pomts. l-homoclinic orbit and l-periodic orbit near T are obtained. Nleanwhile, the bifurcation surfaces and existence regions are also given. Moreover. the above bifurcation results are extended to the case for heteroclinic loop with l saddle points.

关键词： Local coordinates Heteroclinic loop Homoclinic orbit Periodic orbit Bifurcation surface

ON MATRIX UNITARILY INVARIANT NORM CONDITION NUMBER

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Journal of Computational mathematics 1998年第2期16卷 121-128页

作者： Dao-sheng Zheng (department of mathematics, East china normal university, Shanghai 200062, china) E china normal Univ Dept Math Shanghai 200062 Peoples R China

In this paper, the unitarily invariant norm \\.\\ on C-mxn is used. We first discuss the problem under what case, a rectangular matrix A has minimum condition number K(A) = \\A\\ \\A(+)\\, where A(+) designates the Moore-Penrose inverse of A; and under what condition, a square matrix A has minimum condition number for its eigenproblem? Then we consider the second problem, i.e., optimum of K(A) = \\A\\ \\A(-1)\\(2) in error estimation.

关键词： matrix unitarily invariant norm condition number

Extremal problems on the Hua domain of the first type

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Science china mathematics 2005年第z1期48卷 343-354页

作者： SU Jianbing & YIN Weiping mathematics department, Xuzhou normal university, Xuzhou 221116, china mathematics department, Capital normal university, Beijing 100037, china 1. mathematics department Xuzhou Normal University 221116 Xuzhou China 2. mathematics department Capital Normal University 100037 Beijing China

In this paper we study some extremal problems between the Hua domain of the first type and the unit ball.

关键词： extremal problem, Hua domain of the first type, minimal circumscribed Hermitian ellipsoid.

Extremal problems on the generalized Hua domain of the first type

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Progress in Natural Science:Materials International 2006年第4期16卷 352-358页

作者： SU Jianbing and YIN Weiping department of mathematics, Xuzhou normal university, Xuzhou 221116, china department of mathematics, Capital normal university, Beijing 100037, china [a]department of mathematics Xuzhou Normal University Xuzhou China [b]department of mathematics Capital Normal University Beijing China

Some extremal problems between the generalized Hua domain of the first type and the unit ball are studied. The extremal mapping and extremal value in explicit formulas are also obtained.

关键词： extremal problem generalized Hua domain of the first type minimal circumscribed Hermitian ellipsoid.