加权Bergman空间上的Carleson测度与Toeplitz算子

探讨加权Bergman空间Ap()上的Carleson型测度和具有非负测度符号的Toeplitz算子,给出Carleson测度或消没Carleson测度的若干等价描述并用Carleson测度的方法刻画了Toeplitz算子是有界的或紧致的充要条件.     

加权Bergman空间上的Carleson测度与复合算子

本文研究了复平面上单位圆盘D上具有指数型权的加权Bergman空间上的Carleson测度和复合算子。利用Carleson测度的概念分别给出了有界或紧的复合算子的充分必要条件。     

关于加权的帐篷空间

本文建立了加权的帐篷空间，把帐篷空间中的一些主要结果推广到加权的情形，同时刻划了Ap权函数与Carleson测度的一种新的关系。     

球上的对数Carleson测度

本文研究多复变数单位球上的Carleson测度,利用Bloch函数对有界及消没对数Carleson测度进行刻画,得到了在Bloch空间上类似于Hardy空间和Bergman空间上的Carleson定理.并推广的Cesáro算子在Bloch空间上有界和紧的等价条件.     

齐型空间上的Poisson算子与广义Carleson测度

该文在齐型空间上定义了一类广义Carleson测度和Poisson型位势算子，该算子具有与Poisson核相似的性质，研究了该算子在Lp、Hp和Tent空间与Lorentz空间上的有界性.     

利用分数阶Carleson测度刻画BMO~α_-鞅空间

我们利用分数阶Carleson测度给出了BMOα-鞅空间的一个刻画.该刻画表明一个鞅f属于BM Oα-鞅空间当且仅当与该鞅的鞅差有关的某个张量测度为有界α-Carleson测度.利用这个刻画,我们给出了鞅变换算子、均方算子在BMOα-鞅空间上的有界性的非常简洁的证明.此外,我们还证明了在鞅背景下与分数阶Carleson测度有关的Carleson不等式.最后,我们利用分数阶Carleson测度给出了UMD空间的一个刻画.     

Morrey型空间刻画和Carleson测度

定义了解析Morrey型空间H_K~p,并利用H~p空间范数给出了其刻画.还运用Carleson测度刻画了从H_K~p到帐篷型空间J_K~p(μ)嵌入映射的有界性及紧性,其中,权函数K:[0,∞)→[0,∞)是一个右连续且非递减的函数.     

Carleson测度和多项式逼近

设G是复平面C上的单连通区域,在研究G上的Carleson测度和多项式在G上的Hardy空间Hq(G)中的稠密性问题时,建立起了两者之间的一种等价关系．用Carleson测度给出了多项式在Hq(G)中稠密的充要条件,也刻画了所有那些使得在其上的Carleson测度和Carleson不等式等价的单连通区域．     

加权Bergman空间上的Schatten类复合算子

本文利用Carleson测度给出了加权Bergman空间上的复合算子为Schattenp-类算子的充要条件,加权Bergman空间上的复合算子Cφ∈Sp当且仅当对任何r＞0,其中     

Carleson测度和多项式逼近

设G是复平面C上的单连通区域,在研究G上的Carleson测度和多项式在G上的Hardy空间Hq(G)中的稠密性问题时,建立起了两者之间的一种等价关系.用Carleson测度给出了多项式在Hq(G)中稠密的充要条件,也刻画了所有那些使得在其上的Carleson测度和Carleson不等式等价的单连通区域.     

QCLkR空间与QCLkS空间

引入了QCLkR空间和QCLkS空间的概念,以局部自反原理为工具证明了QCLkR空间和QCLkS空间的对偶关系.利用切片给出了QCLkR空间和QCLkS空间的特征刻画,并讨论了它们与其它凸性和光滑性的关系,所得结果进一步完善了关于Banach空间凸性与光滑性的研究.     

Affine Spaces within Projective Spaces

We endow the set of complements of a fixed subspace of a projective space with the structure of an affine space, and show that certain lines of such an affine space are affine reguli or cones over affine reguli. Moreover, we apply our concepts to the problem of describing dual spreads. We do not assume that the projective space is finite-dimensional or pappian.     

局部强紧空间的Hoare空间与Smyth空间

本文主要讨论局部强紧空间的性质,特别是其Hoare空间和Smyth空间的性质,证明了T_0空间为局部强紧空间的当且仅当其Hoare空间为局部强紧空间,局部强紧空间的Smyth空间为C-空间.对于强局部紧空间,我们有类似的结论.     

调和H~p空间和混合范数空间

设Ｄ是一具有Ｃ边界的有界区域．本文就Ｄ上的调和Ｈａｒｄｙ空间和调和混合范数空间,建立了若干互相之间的连续嵌入定理．     

p-Banach Spaces and p-Totally Convex Spaces

We introduce the categories Vec _p of p-normed vector spaces, Ban _p of _p -Banach spaces, AC _p of _p -absolutely and TC _p of _p -totally convex spaces (0 < p 1). It will be shown that TC _p (AC _p ) is the Eilenberg–Moore category of Ban _p (Vec _p ). Then congruence relations on TC _p (AC _p )-spaces are studied. There are many differences between TC _p (AC _p )-spaces and totally (absolutely) convex spaces (i.e. p = 1) (Pumplün and Röhrl, 1984, 1985), which will become apparent in Section 4.     

Approach Spaces, Limit Tower Spaces, and Probabilistic Convergence Spaces

The category LTS of limit tower spaces is defined and shown to be isomorphic to the category CAP of convergence approach spaces. The full subcategory of LTS determined by the objects satisfying a diagonal axiom due to Cook and Fischer is shown to be isomorphic to the category AP of approach spaces. A family of isomorphisms is also obtained between LTS and certain full subcategories of the category PCS of probabilistic convergence spaces.     

Morrey-Sobolev Spaces on Metric Measure Spaces

In this article, the authors introduce the Newton-Morrey-Sobolev space on a metric measure space (??, d, μ). The embedding of the Newton-Morrey-Sobolev space into the Hölder space is obtained if ?? supports a weak Poincaré inequality and the measure μ is doubling and satisfies a lower bounded condition. Moreover, in the Ahlfors Q-regular case, a Rellich-Kondrachov type embedding theorem is also obtained. Using the Haj?asz gradient, the authors also introduce the Haj?asz-Morrey-Sobolev spaces, and prove that the Newton-Morrey-Sobolev space coincides with the Haj?asz-Morrey-Sobolev space when μ is doubling and ?? supports a weak Poincaré inequality. In particular, on the Euclidean space \({\mathbb R}^n\) , the authors obtain the coincidence among the Newton-Morrey-Sobolev space, the Haj?asz-Morrey-Sobolev space and the classical Morrey-Sobolev space. Finally, when (??, d) is geometrically doubling and μ a non-negative Radon measure, the boundedness of some modified (fractional) maximal operators on modified Morrey spaces is presented; as an application, when μ is doubling and satisfies some measure decay property, the authors further obtain the boundedness of some (fractional) maximal operators on Morrey spaces, Newton-Morrey-Sobolev spaces and Haj?asz-Morrey-Sobolev spaces.