The Representation Theorem of onto Isometric Mappings between Two Unit Spheres of l^1（Γ） Type Spaces and The Application to the Isometric Extension Problem

In this paper, we first derive the representation theorem of onto isometric mappings in the unit spheres of l^1（Γ） type spaces, and then conchlde that such mappings can be extended to the whole space as real linear isometries by using a previous result of the author.     

On Linearly Isometric Extensions for 1-Lipschitz Mappings Between Unit Spheres of ALP-spaces （p 〉 2）

In this paper, we show that if Vo is a 1-Lipschitz mapping between unit spheres of two ALP-spaces with p 〉 2 and -Vo（S1（LP）） C Vo（S1（LP））, then V0 can be extended to a linear isometry defined on the whole space. If 1 〈 p 〈 2 and Vo is an ＂anti-l-Lipschitz＂ mapping, then Vo can also be linearly and isometrically extended.     

On the Extension of Isometries between Unit Spheres of E and C（Ω）

In this paper,we study the extension of isometries between the unit spheres of some Banach spaces E and the spaces C(Ω). We obtain that if the set sm.S1(E) of all smooth points of the unit sphere S1(E) is dense in S1(E),then under some condition,every surjective isometry V0 from S1(E) onto S1(C(Ω)) can be extended to be a real linearly isometric map V of E onto C(Ω).From this resultwe also obtain some corollaries. This is the first time we study this problem on different typical spaces,and the method of proof is also very different too.     

On the Maximality of the Sum of Two Maximal Monotone Mappings in Banach Spaces

Let (X, X) be a pair of real reflexive Banach spaces,and X be X's dual space.We assume without loss of generality that X and X are strictly convex(See Asplund [1]).Let A and B be two maximal monotone mappings from X into 2~x.Attoueh [2] has shown that when X=X is a real Hilbert space,if Int(D(A)-     

On Extension of Isometries Between the Unit Spheres of Normed Space E and lP（p 〉 1）

In this paper, we study the extension of isometries between the unit spheres of normed space E and lP（p 〉 1）. We arrive at a conclusion that any surjective isometry between the unit sphere of normed space lP（p 〉 1） and E can be extended to be a linear isometry on the whole space lP（p 〉 1） under some condition.     

A Note on Linear Extension of Into-Isometries Between Two Unit Spheres of Atomic AL^p-Space （0 〈 p 〈∞）

In this paper, we shall present a short and simple proof on the isometric linear extension problem of into-isometries between two unit spheres of atomic abstract L^p-spaces （0 〈 p 〈 ∞）.     

Extension of isometries between the unit spheres of complex l(Γ)(p>1)spaces

In this paper, we study the extension of isometries between the unit spheres of complex Banach spaces l^p(Γ) and l^p(Δ)(p > 1). We first derive the representation of isometries between the unit spheres of complex Banach spaces l^p(Γ) and l^p(Δ). Then we arrive at a conclusion that any surjective isometry between the unit spheres of complex Banach spaces l^p(Γ)and l^p(Δ) can be extended to be a linear isometry on the whole space.     

Extension of isometries on the unit sphere of l~p (Γ) space

In this paper,we obtain that every isometry from the unit sphere S(l p (Γ)) of l p (Γ) (1 p ∞,p≠2) onto the unit sphere S(E) of a Banach space E can be extended to be a (real) linear isometry of l p (Γ) onto E,so,we give an affirmative answer to the corresponding Tingley's problem.     

空间l~p(Γ)(1

蒋艳  陈绍雄 《数学学报》2011,(4):687-696

On the reduction (mod 1) of completely monotone functions (0, ∞)

Summary The Euler-Maclaurin summation formula and its harmonic analysis (Poisson) are applied to the case of functions which are completely monotone on an open half-line. What thus results is a curious class of Fourier series, which can be determined explicitly and which represent completely monotone functions on the first half of the period. A by-product is the complete monotony (on the first half-period) of the Bernoulli functions, whether the index is integral or fractional.     

Weakly Sequential Completeness of L(l_p,X)and K(l_p,X)(1

《数学研究与评论》1992,(3)

Banach Spaces Which are Isometric to Subspaces of c_0(Γ)

In this paper, we give a number of characterizations for a Banach space X which is isometric to a subspace of c_0, or, c_0(Γ), successively, in terms of extreme points of its dual unit ball BX~*, Fréchet and Gateaux derivatives of its norm, or, in terms of w~*-strongly exposed points and w~*-exposed points of BX~*.     

On a Hardy Type General Weighted Inequality in Spaces L p(·)

A Hardy type two-weighted inequality is investigated for the multidimensional Hardy operator in the norms of generalized Lebesgue spaces L ^p(·). Equivalent necessary and sufficient conditions are found for the ${L^{p(\cdot)} \longrightarrow L^{q(\cdot)}}A Hardy type two-weighted inequality is investigated for the multidimensional Hardy operator in the norms of generalized Lebesgue spaces L ^p(·). Equivalent necessary and sufficient conditions are found for the L^p(·) ? L^q(·){L^{p(\cdot)} \longrightarrow L^{q(\cdot)}} boundedness of the Hardy operator when exponents q(0) < p(0), q(∞) < p(∞). It is proved that the condition for such an inequality to hold coincides with the condition for the validity of two-weighted Hardy inequalities with constant exponents if we require of the exponents to be regular near zero and at infinity.     

On the Global Pinching Theorem for the Minimal Submanifolds in the Unit Spheres S~(n+p)(1)

J.Simons proved that if a minimal submanifold,M~n in the unit sphere S~(n+p)(1)satisfies,|B|~2相似文献   

A Characterization of l + 1(Γ)

In this article we give necessary and sufficient conditions in order a closed cone of a Banach space E to be isomorphic to the positive cone l ₁ ⁺(Γ) of an l ₁(Γ) space. This problem has applications in the theory of Banach spaces as in the characterization of reflexive spaces and also on the problem of the embeddability of 1in Banach spaces.     

空间lp(Γ)(p＞1)的单位球面间等距算子的延拓

首先得到lp(Γ)(p＞1,p≠2)单位球面之间(满)等距算子的表现定理,然后利用作者过去一个结果导出:上述算子均可延拓为全空间上的(实)线性等距算子.     

L_[0,1]~p(1

梅雪峰  周颂平 《数学进展》2005,(6)

A Local Hlder Estimate of(K_1, K_2)-Quasiconformal Mappings between Hypersurfaces

In this paper, we prove a local H¨older estimate of(K1, K2)-quasiconformal mappings between n-dimensional hypersurfaces of Rn+1under an assumption of bounded mean curvature of the original hypersurface M. With some new ingredients of the isoperimetric inequality and the co-area formula on manifolds, we extend Simon's work of quasiconformal mappings on surfaces of R3 to the setting of n-dimensional hypersurfaces of Rn+1.     

两个$l^p(\Gamma)$型空间单位球面之间的1-Lipschitz映射的延拓($1

方习年 《数学研究及应用》2009,29(4):687-692