Let X be a complex Banach space and let B and C be two closed linear operators on X satisfying the condition D(B)?D(C),and let d∈L^(1)(R_(+))and 0≤β<α≤2.We characterize the well-posedness of the fractional int...Let X be a complex Banach space and let B and C be two closed linear operators on X satisfying the condition D(B)?D(C),and let d∈L^(1)(R_(+))and 0≤β<α≤2.We characterize the well-posedness of the fractional integro-differential equations D^(α)u(t)+CD^(β)u(t)=Bu(t)+∫_(-∞)td(t-s)Bu(s)ds+f(t),(0≤t≤2π)on periodic Lebesgue-Bochner spaces L^(p)(T;X)and periodic Besov spaces B_(p,q)^(s)(T;X).展开更多
设X为一复Banach空间,f:D→X为一个X-值解析函数,f(z)=sum from n≥0(a_nz^n),a_n∈X,设C(f)(z)=sum from n≥0((a_0+a_1+…+a_n)/(n+1)z^n)A(f)(z)=sum from n≥0(sum from k=n to ∞(a_k/(k+1))z^n本文证明了对于任意的1≤p<∞以及...设X为一复Banach空间,f:D→X为一个X-值解析函数,f(z)=sum from n≥0(a_nz^n),a_n∈X,设C(f)(z)=sum from n≥0((a_0+a_1+…+a_n)/(n+1)z^n)A(f)(z)=sum from n≥0(sum from k=n to ∞(a_k/(k+1))z^n本文证明了对于任意的1≤p<∞以及复Banach空间X,C为从H^p(X)到H^p(X)的有界线性算子;对于任意的1<p≤∞以及复Banach空间X,A为从(?)(X)到(?)(X)的有界线性算子.这些结果推广了A.G.Siskakis的结果.展开更多
The authors establish operator-valued Fourier multiplier theorems on Triebel spaces on R^N, where the required smoothness of the multiplier functions depends on the dimension N and the indices of the Triebel spaces. T...The authors establish operator-valued Fourier multiplier theorems on Triebel spaces on R^N, where the required smoothness of the multiplier functions depends on the dimension N and the indices of the Triebel spaces. This is used to give a sufficient condition of the maximal regularity in the sense of Triebel spaces for vector-valued Cauchy problems with Dirichlet boundary conditions.展开更多
We study Hlder continuous solutions for the second order integro-differential equations with infinite delay （P1）： u′′（t）＋cu′（t）＋∫t-∞β（t-s）u′（s）ds＋∫t-∞γ（t-s）u（s）ds = Au（t）-∫t-∞δ（t-s）A...We study Hlder continuous solutions for the second order integro-differential equations with infinite delay （P1）： u′′（t）＋cu′（t）＋∫t-∞β（t-s）u′（s）ds＋∫t-∞γ（t-s）u（s）ds = Au（t）-∫t-∞δ（t-s）Au（s）ds ＋ f（t）on the line R, where 0 〈 α 〈 1, A is a closed operator in a complex Banach space X, c ∈ C is a constant, f ∈ Cα（R,X） and β,γ,δ∈L1（R＋）.Under suitable assumptions on the kernels β, γ and δ, we completely characterize the Cα- well-posedness of （P_1） by using operator-valued Cα-Fourier multipliers.展开更多
In this paper, we show that J-convex and PSH-convex are different notions for closed bounded subsets in complex Banach space. Precisely, we show that a complex Banach space X is infinite dimensional if and only if the...In this paper, we show that J-convex and PSH-convex are different notions for closed bounded subsets in complex Banach space. Precisely, we show that a complex Banach space X is infinite dimensional if and only if there exists a closed bounded J-convex subset which is not PSH-convex.展开更多
In the papaer, it is defined the analytic Krein-Milman property for plurisubharmonic convex subsets in complex Banach spaces and studied the relation between it and the analytic Radon-Nikodym property.
The following result is established:let X be a Banach space without the Radon-Nikodym property,there exists a uniformly bounded harmonic function f defined onthe open unit disk of C with values in X,such that for almo...The following result is established:let X be a Banach space without the Radon-Nikodym property,there exists a uniformly bounded harmonic function f defined onthe open unit disk of C with values in X,such that for almost allθ∈[0,2π],（?）f(re<sup>iθ</sup>)does not exist.展开更多
基金the NSF of China(12171266,12171062)the NSF of Chongqing(CSTB2022NSCQ-JQX0004)。
文摘Let X be a complex Banach space and let B and C be two closed linear operators on X satisfying the condition D(B)?D(C),and let d∈L^(1)(R_(+))and 0≤β<α≤2.We characterize the well-posedness of the fractional integro-differential equations D^(α)u(t)+CD^(β)u(t)=Bu(t)+∫_(-∞)td(t-s)Bu(s)ds+f(t),(0≤t≤2π)on periodic Lebesgue-Bochner spaces L^(p)(T;X)and periodic Besov spaces B_(p,q)^(s)(T;X).
文摘设X为一复Banach空间,f:D→X为一个X-值解析函数,f(z)=sum from n≥0(a_nz^n),a_n∈X,设C(f)(z)=sum from n≥0((a_0+a_1+…+a_n)/(n+1)z^n)A(f)(z)=sum from n≥0(sum from k=n to ∞(a_k/(k+1))z^n本文证明了对于任意的1≤p<∞以及复Banach空间X,C为从H^p(X)到H^p(X)的有界线性算子;对于任意的1<p≤∞以及复Banach空间X,A为从(?)(X)到(?)(X)的有界线性算子.这些结果推广了A.G.Siskakis的结果.
文摘The authors establish operator-valued Fourier multiplier theorems on Triebel spaces on R^N, where the required smoothness of the multiplier functions depends on the dimension N and the indices of the Triebel spaces. This is used to give a sufficient condition of the maximal regularity in the sense of Triebel spaces for vector-valued Cauchy problems with Dirichlet boundary conditions.
基金supported by the NSF of Chinathe Specialized Research Fund for the Doctoral Program of Higher Education
文摘We study Hlder continuous solutions for the second order integro-differential equations with infinite delay （P1）： u′′（t）＋cu′（t）＋∫t-∞β（t-s）u′（s）ds＋∫t-∞γ（t-s）u（s）ds = Au（t）-∫t-∞δ（t-s）Au（s）ds ＋ f（t）on the line R, where 0 〈 α 〈 1, A is a closed operator in a complex Banach space X, c ∈ C is a constant, f ∈ Cα（R,X） and β,γ,δ∈L1（R＋）.Under suitable assumptions on the kernels β, γ and δ, we completely characterize the Cα- well-posedness of （P_1） by using operator-valued Cα-Fourier multipliers.
文摘In this paper, we show that J-convex and PSH-convex are different notions for closed bounded subsets in complex Banach space. Precisely, we show that a complex Banach space X is infinite dimensional if and only if there exists a closed bounded J-convex subset which is not PSH-convex.
文摘In the papaer, it is defined the analytic Krein-Milman property for plurisubharmonic convex subsets in complex Banach spaces and studied the relation between it and the analytic Radon-Nikodym property.
文摘The following result is established:let X be a Banach space without the Radon-Nikodym property,there exists a uniformly bounded harmonic function f defined onthe open unit disk of C with values in X,such that for almost allθ∈[0,2π],（?）f(re<sup>iθ</sup>)does not exist.
