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| 1 | Solutions of second order degenerate integro-differential equations in vector-valued function spaces显示文摘We study the well-posedness of the second order degenerate integro-differential equations(P2):(Mu)(t)+α(Mu)(t) = Au(t)+ft-∞ a(ts)Au(s)ds + f(t),0t2π,with periodic boundary conditions M u(0)=Mu(2π),(Mu)(0) =(M u)(2π),in periodic Lebesgue-Bochner spaces Lp(T,X),periodic Besov spaces B s p,q(T,X) and periodic Triebel-Lizorkin spaces F s p,q(T,X),where A and M are closed linear operators on a Banach space X satisfying D(A) D(M),a∈L1(R+) and α is a scalar number.Using known operatorvalued Fourier multiplier theorems,we completely characterize the well-posedness of(P2) in the above three function spaces. | BU ShangQuan CAI Gang | 2013 | Science China Mathematics2013，56，5： | 4 |
| 2 | Maximal regularity of second order delay equations in Banach spaces显示文摘We give necessary and sufficient conditions of Lp-maximal regularity(resp.B sp ,q-maximal regularity or F sp ,q-maximal regularity) for the second order delay equations:u″(t)=Au(t) + Gu't + F u t + f(t), t ∈ [0, 2π] with periodic boundary conditions u(0)=u(2π), u′(0)=u′(2π), where A is a closed operator in a Banach space X,F and G are delay operators on Lp([-2π, 0];X)(resp.Bsp ,q([2π, 0];X) or Fsp,q([-2π, 0;X])). | BU ShangQuan ? & FANG Yi Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China | 2010 | Science China Mathematics2010，53，1： | 2 |
| 3 | Well-posedness of degenerate differential equations in Hiilder continuous function spaces显示文摘 | Shangquan BU | 2015 | Frontiers of Mathematics in China2015，10，2： | 1 |
| 4 | THE EXISTENCE OF JENSEN BOUNDARY POINTS IN COMPLEX BANACH SPACES显示文摘We show that a complex Banach space X has the analytic Radon-Nikodym property if and only if every non-empty closed bounded subset of X has a Jensen boundary point. If we suppose furthermore that X is isomorphic to its square X2, X has the analytic Radon-Nikodym property if and only if every non-empty Jensen convex subset of X has a Jensen boundary poifit. | BU Shangquan (Department of Applied Mathematics, Tsinghua University, Beijing 100084, China) | 1999 | Systems Science and Mathematical Sciences1999，12，1： | 0 |
| 5 | THE EXISTENCE OF RADIAL LIMITS OF ANALYTIC FUNCTIONS IN BANACH SPACES显示文摘Let X be a complex Banach space without the analytic Radon-Nikodym property. The author shows that G = {f∈H∞(D,X) there exists∈> 0, such that for almost allθ∈[0, 2], lim sup f(reiθ) - f(seiθ)≥∈ } is a dense open subset of H∞(D, X). It is also shown that for every open subset B of T, there exists F∈H∞ (D, X), such that F has boundary values everywhere on Bc and F has radial limits nowhere on B. When A is a measurable subset of T with positive measure, there exists f∈H∞ (D, X), such that f has nontangential limits almost everywhere on Ac and f has radial limits almost nowhere on A. | BU SHANGQUAN Department of Applied Mathematics, Tsinghua University, Beijing 100084, China. E-mail: sbu@math.tsinghua.edu.cn | 2001 | Chinese Annals of Mathematics,Series B2001，22，4： | 0 |
| 6 | A COUNTER-EXAMPLE CONCERNING THE ANALYTIC RADON-NIKODYM PROPERTY显示文摘ACOUNTER-EXAMPLECONCERNINGTHEANALYTICRADON-NIKODYMPROPERTY￥BUSHANGQUAN(DepartmentofAppliedMathematics,QinghuaUniversityBeijin... | BU SHANGQUAN (Department of Applied Mathematics, Qinghua University Beijing 100084, China.Project supported by the National Natural Science Foundation of China.) | 1995 | Chinese Annals of Mathematics,Series B1995，16，1： | 0 |
| 7 | On operator-valued Fourier multipliers显示文摘We give a simpler proof of a result on operator-valued Fourier multipliers on Lp([0, 2π]d; X) using an induction argument based on a known result when d= 1. | BU Shangquan | 2006 | Science China Mathematics2006，49，4： | 0 |
| 8 | Operator-Valued Fourier Multipliers on Multi-dimensional Hardy Spaces显示文摘The author establishes operator-valued Fourier multiplier theorems on multi-dimensional Hardy spaces Hp(Td;X),where 1 ≤ p < ∞,d ∈ N,and X is an AUMD Banach space having the property (α).The suffcient condition on the multiplier is a Marcinkiewicz type condition of order 2 using Rademacher boundedness of sets of bounded linear operators.It is also shown that the assumption that X has the property (α) is necessary when d ≥ 2 even for scalar-valued multipliers.When the underlying Banach space does not have the property (α),a suffcient condition on the multiplier of Marcinkiewicz type of order 2 using a notion of d-Rademacher boundedness is also given. | Shangquan BU | 2011 | Chinese Annals of Mathematics,Series B2011，32，2： | 0 |
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