On the random conjugate spaces of a random locally convex module

Theoretically speaking, there are four kinds of possibilities to define the random conjugate space of a random locally convex module. The purpose of this paper is to prove that among the four kinds there are only two which are universally suitable for the current development of the theory of random conjugate spaces. In this process, we also obtain a somewhat surprising and crucial result: if the base (Ω, F , P ) of a random normed module is nonatomic then the random normed module is a totally disconnected topological space when it is endowed with the locally L0 -convex topology.     

高维单形的等距共轭点性质初探(英文)

In this paper, the concept of the equidistant conjugate points of a triangle to the n-dimensional Euclidean space is extended. The concept of equidistant conjugate point in high dimensional simplex is defined, and the property of the equidistant conjugate points of a triangle is generalized to high dimensional simplex.     

Riesz Transforms Associated with Schrdinger Operators Acting on Weighted Hardy Spaces

Let L =-? + V be a Schrdinger operator acting on L2(Rn), n ≥ 1, where V ≡ 0 is a nonnegative locally integrable function on Rn. In this article, we will intropduce weighted Hardy spaces H L(w) associated with L by means of the square function and then study their atomic decomposition theory. We will also show that the Riesz transform ?L-1/2associated with L is bounded from our new space Hp L(w) to the classical weighted Hardy space Hp(w) when n/(n +1) p 1 and w ∈ A1∩ RH(2/p)′.     

A NOTE ON THE WALSH-FEJR MEANS

The main aim of this paper is to prove that the maximal operator σ # is not bounded from the martingale Hardy space Hp (G) to the martingale Hardy space Hp (G) for 0 < p ≤ 1.     

Image space analysis for variational inequalities with cone constraints and applications to traffic equilibria

In this paper,the image space analysis (for short,ISA) is employed to investigate variational in- equalities (for short,VI) with cone constraints.Linear separation for VI with cone constraints is characterized by using the normal cone to a regularization of the image,and saddle points of the generalized Lagrangian func- tion.Lagrangian-type necessary and sufficient optimality conditions for VI with cone constraints are presented by using a separation theorem.Gap functions and weak sharpness for VI with cone constraints are also investi- gated.Finally,the obtained results are applied to standard and time-dependent traffic equilibria introduced by Daniele,Maugeri and Oettli.     

Special John-Nirenberg-Campanato spaces via congruent cubes

Let p ∈ [1, ∞), q ∈ [1, ∞), α∈ R, and s be a non-negative integer. Inspired by the space JNp introduced by John and Nirenberg(1961) and the space B introduced by Bourgain et al.(2015), we introduce a special John-Nirenberg-Campanato space JN^con_(p,q,s) over Rⁿ or a given cube of R;with finite side length via congruent subcubes, which are of some amalgam features. The limit space of such spaces as p →∞ is just the Campanato space which coincides with the space BMO(the space of functions with bounded mean oscillations)when α = 0. Moreover, a vanishing subspace of this new space is introduced, and its equivalent characterization is established as well, which is a counterpart of the known characterization for the classical space VMO(the space of functions with vanishing mean oscillations) over Rⁿ or a given cube of Rⁿ with finite side length.Furthermore, some VMO-H¹-BMO-type results for this new space are also obtained, which are based on the aforementioned vanishing subspaces and the Hardy-type space defined via congruent cubes in this article. The geometrical properties of both the Euclidean space via its dyadic system and congruent cubes play a key role in the proofs of all these results.     

MULTIPLIERS AND TENSOR PRODUCTS OF L（p, q） LORENTZ SPACES

Let G be a locally compact abelian group. The main purpose of this article is to find the space of multipliers from the Lorentz space L(p1, q1)(G) to L(p21,q21)(G). For this reason, the authors define the space Ap1,q1p2,q2(G), discuss its properties and prove that the space of multipliers from L(p1,q1)(G) to L(p21,q21)(G) is isometrically isomorphic to the dual of Ap1,q1p2q2(G).     

A note on Thewalsh-Fejér means

The main aim of this paper is to prove that the maximal operator σ # is not bounded from the martingale Hardy space Hp (G) to the martingale Hardy space Hp (G) for 0 < p ≤ 1.     

RIEMANN SUMMABILITY OF MULTI-DIMENSIONAL TRIGONOMETRIC-FOURIER SERIES

The d-dimensional classical Hardy spaces H_p (T~d) are introduced and it is shown that themaximal operator of the Riemann sums of a distribution is bounded from H_p(T~d)to L_p(T~2)(d/(d+1)相似文献   

Complex convexity of Musielak-Orlicz sequence spaces equipped with the p-Amemiya norm北大核心CSCD

We mainly discuss the complex convexity of Musielak-Orlicz sequence spaces equipped with the p-Amemiya norm. It is obtained that for any Musielak-Orlicz sequence space equipped with the p-Amemiya norm when 1 ≤ p < ∞, complex strongly extreme points of the unit ball coincide with complex extreme points of the unit ball. Moreover, criteria for them in above spaces are given. Criteria for complex rotundity and complex mid-point locally uniform convexity of above spaces are also deduced. ©, 2015, Chinese Academy of Sciences. All right reserved.     

Derived space of L p (G, H)

Let G denote a locally compact abelian group and H a separable Hilbert space. Let L _p (G, H), 1 ≤ p < ∞, be the space of H-valued measurable functions which are in the usual L _p space. Motivated by the work of Helgason [1], Figa-Talamanca [11] and Bachelis [2, 3], we have defined the derived space of the Banach space L _p (G, H) and have studied its properties. Similar to the scalar case, we prove that if G is a noncompact, locally compact abelian group, then L _p ⁰ (G, H) = {0} holds for 1 ≤ p < 2. Let G be a compact abelian group and Γ be its dual group. Let S _p (G, H) be the L ₁(G) Banach module of functions in L _p (G, H) having unconditionally convergent Fourier series in L _p -norm. We show that S _p (G, H) coincides with the derived space L _p ⁰ (G, H), as in the scalar valued case. We also show that if G is compact and abelian, then L _p ⁰ (G, H) = L ₂(G, H) holds for 1 ≤ p ≤ 2. Thus, if F ∈ L _p (G, H), 1 ≤ p < 2 and F has an unconditionally convergent Fourier series in L _p -norm, then F ∈ L ₂(G, H). Let Ω be the set of all functions on Γ taking only the values 1, ?1 and Ω* be the set of all complex-valued functions on Γ having absolute value 1. As an application of the derived space L _p ⁰ (G, H), we prove the following main result of this paper. Let G be a compact abelian group and F be an H-valued function on the dual group Γ such that $$ \sum \omega (\gamma )F(\gamma )\gamma $$ is a Fourier-Stieltjes series of some measure µ ∈ M(G, H) for every scalar function ω such that |ω(γ)| = 1. Then F ∈ l ²(Γ, H).     

The maximal Fejér operator on the spacesH p (R×···×R)

It is shown that the maximal operator of the Fejér means of a tempered distribution is bounded from thed-dimensional Hardy spaceH _p (R×···×R) toL _p (R ^d ) (1/2<p<∞) and is of weak type (H ₁ ^?i ,L ₁) (i=1,…,d), where the Hardy spaceH ₁ ^?i is defined by a hybrid maximal function. As a consequence, we obtain that the Fejér means of a functionf ∈H ₁ ^?i ?L(logL) ^d?1 converge a.e. to the function in question. Moreover, we prove that the Fejér means are uniformly bounded onH _p (R×···×R) whenever 1/2<p<∞. Thus, in casef ∈H _p (R×···×R) the Fejér means converge tof inH _p (R×···×R) norm. The same results are proved for the conjugate Fejér means, too.     

Regular Submanifolds in Conformal Space ${\mathbb Q}^n_p$

The authors study the regular submanifolds in the conformal space Q_p~n and introduce the submanifold theory in the conformal space Q_p~n.The first variation formula of the Willmore volume functional of pseudo-Riemannian submanifolds in the conformal spaceQ_p~n is given.Finally,the conformal isotropic submanifolds in the conformal space Q_p~n are classified.     

New criteria for boundedness and compactness of weighted composition operators mapping into the Bloch space

Let ψ and φ be analytic functions on the open unit disk $\mathbb{D}$ with φ( $\mathbb{D}$ ) ? $\mathbb{D}$ . We give new characterizations of the bounded and compact weighted composition operators W _ψ,? from the Hardy spaces H ^p , 1 ≤ p ≤ ∞, the Bloch space B, the weighted Bergman spaces A _α ^p , α > ? 1,1 ≤ p < ∞, and the Dirichlet space $\mathcal{D}$ to the Bloch space in terms of boundedness (respectively, convergence to 0) of the Bloch norms of W _ψ,? f for suitable collections of functions f in the respective spaces. We also obtain characterizations of boundedness for H ¹ as well as of compactness for H ^p , 1 ≤ p < ∞, and $\mathcal{D}$ purely in terms of the symbols ψ and φ.     

Commutator of hypersingular integral with rough kernels on Sobolev spaces

In this paper, the authors give the boundedness of the commutator of hypersingular integral T γ from the homogeneous Sobolev space Lpγ (Rn) to the Lebesgue space Lp(Rn) for 1p∞ and 0 γ min{ n/2 , n/p }.     

On the primes withp n+1 -p n = 8 and the Sum of their Reciprocals

We introduce the counting function π _2,8 ^* (x) of the primes with difference 8 between consecutive primes ( ****p _n,p_n+1 =p _n + 8) can be approximated by logarithm integralLi _2,8 ^* . We calculate the values of π _2,8 ^* (x) and the sumC _2,8(x) of reciprocals of primes with difference 8 between consecutive primes (p _n,p_n+1 =p _n +8)) wherex is counted up to 7 x 10¹⁰. From the results of these calculations, we obtain π _2,8 ^* (7 x 10¹⁰) = 133295081 andC _2,8(7 x 10¹⁰) = 0.3374 ±2.6 x 10^-4.     

Description of traces of functions in the Sobolev space with a Muckenhoupt weight

We characterize the trace of the Sobolev space W _p ^l (? ⁿ , γ) with 1 < p < ∞ and weight γ ∈ A _p ^loc (? ⁿ ) on a d-dimensional plane for 1 ≤ d < n. It turns out that for a function φ to be the trace of a function f ∈ W _p ^l (? ⁿ , γ), it is necessary and sufficient that φ belongs to a new Besov space of variable smoothness, $\overline B _p^l \left( {\mathbb{R}^d ,\left\{ {\gamma _{k,m} } \right\}} \right)$ , constructed in this paper. The space $\overline B _p^l \left( {\mathbb{R}^d ,\left\{ {\gamma _{k,m} } \right\}} \right)$ is compared with some earlier known Besov spaces of variable smoothness.     

The relations among the three kinds of conditional risk measures

Let(Ω,E,P)be a probability space,F a sub-σ-algebra of E,Lp(E)(1 p+∞)the classical function space and Lp F(E)the L0(F)-module generated by Lp(E),which can be made into a random normed module in a natural way.Up to the present time,there are three kinds of conditional risk measures,whose model spaces are L∞(E),Lp(E)(1 p+∞)and Lp F(E)(1 p+∞)respectively,and a conditional convex dual representation theorem has been established for each kind.The purpose of this paper is to study the relations among the three kinds of conditional risk measures together with their representation theorems.We first establish the relation between Lp(E)and Lp F(E),namely Lp F(E)=Hcc(Lp(E)),which shows that Lp F(E)is exactly the countable concatenation hull of Lp(E).Based on the precise relation,we then prove that every L0(F)-convex Lp(E)-conditional risk measure(1 p+∞)can be uniquely extended to an L0(F)-convex Lp F(E)-conditional risk measure and that the dual representation theorem of the former can also be regarded as a special case of that of the latter,which shows that the study of Lp-conditional risk measures can be incorporated into that of Lp F(E)-conditional risk measures.In particular,in the process we find that combining the countable concatenation hull of a set and the local property of conditional risk measures is a very useful analytic skill that may considerably simplify and improve the study of L0-convex conditional risk measures.∞     

On the multipliers of Fourier series with respect to the Haar system

qV РАБОтЕ РАссМАтРИВАУ тсь МУльтИплИкАтИВН ыЕ пРЕОБРАжОВАНИь РьДО В ФУРьЕ-хААРА. ИжУЧЕНы слЕДУУЩИЕ кл Ассы МУльтИплИкАтОР ОВ: (H _p ^α ,H _q ^β ), (H _p ^α ,L ^q ) И (с, с).     

Remarks on Banaschewski-Fomin-Shanin extensions

The notion ofB ^*-continuous andB _c ^* -continuous maps is introduced. The problem of epireflection of Banaschewski-Fomin-Shanin extension for a general Hausdorff space is investigated with the help of_p B ^* and_P B _c ^* -continuous maps.