单位球上Bloch型空间到F(p,q,s)空间的Volterra复合算子

记H(B)为C~n中单位球B上的解析函数空间.设φ为B到自身的解析映射,g∈H(B),μ为正规权,定义Volterra复合算子为(V_φ~gf)(z)=∫_0~1f(φ(tz))Rg(tz)dt/t.本文考虑Volterra复合算子V_φ~g从B_μ或B_(μ,0)空间到F(p,q,s)或F_0(p,q,s)空间上的有界性和紧性,得出了算子V_φ~g:B_μ(B_(μ,0))→F(p,q,s)或B_μ(B_(μ,0))→F_0(p,q,s)的紧性与有界性等价.同时,也给出了算子V_φ~g从B~α或B_0~α空间到F(p,q,s)或F_0(p,q,s)空间上的紧性和有界性刻画.     

从B~0到E(p，q)和E_0(p，q)空间的复合算子(英文)

设φ是单位园盘D到自身的解析映射,X是D上解析函数的Banach空间,对f∈X,定义复合算子C_φ∶C_φ)(f)=fφ．我们利用从B~0到E(p,q)和E_0(p,q)空间的复合算子研究了空间E(p,q)和E_0(p,q),给出了一个新的特征．     

Besov空间和Zygmund空间上的复合算子

讨论单位圆盘上Besov空间B（p,q）和Zygmund空间Z及小Zygmund空间Z_0之间的复合算子,得到了B（p,q）到Z（Z_0）的复合算子以及Z（Z0）到B（p,q）的复合算子有界或紧的充要条件。     

F(p,q,s)到B_μ广义复合算子的差分

令B为N维复空间C~N的开单位球,φ是B上的解析自映射,g是B上的解析函数,且g(0)=0,则广义复合算子定义为C_φ~g(f)(z)=∫_0~1Rf(φ(tz))g(tz)(dt)/t.本文主要研究单位球上从F(p,q,s)空间到加权Bloch空间B_μ的广义复合算子的差分有界性与紧致性.     

p-Bloch空间上的复合算子和加权复合算子

本文系统地讨论了单位圆中p-Bloch空间上复合算子T1,δ的有界性和紧性以及加权复合算子Tφ,δ的有界性,同时也在小p-Bloch空间上讨论了复合算子T1,φ的有界性问题.主要得到以下结论: (i)Tφ,δ是空间βp到βq的有界算子之充要条件; (ii)T1,φ是空间βp到βq的紧算子之充要条件; (iii)T1,φ是空间βp0到βq0的有界算子之充要条件等.从空间或算子上扩展了文[1,4]的相应结论.     

广义Bergman空间上的紧复合算子

首先证明广义Bergman空间A_(N,α)~p,(α-n-1,p0)上的复合算子C_φ的有界性和紧性是不依赖于p的,进而证明了若对某个q0和-n-1βα,C_φ在A_(N,β)~α上有界,则C_φ在A_(N,α)~p,α(α-n-1,p0)上是紧的当且仅当lim|z|→1-1-(|z|~2/1-|φ(1)|~2)=0.     

关于从混合模空间到小Zygmund空间的Volterra型复合算子

利用混合模空间H(p,q,φ)中函数的高阶导数的估计、解析函数的性质与算子理论,给出了从混合模空间H(p,q,φ)到小Zygmund空间的Volterra型复合算子的有界性和紧性的特征,获得了几个充要条件.     

从混合模空间到Zygmund空间的Volterra型复合算子

本文利用混合模空间H(p,q,φ)中函数的高阶导数的估计,通过构造一些新的检验函数,运用解析函数的性质与算子理论,给出了从混合模空间H(p,q,φ)到Zygmund空间的Volterra型复合算子的有界性和紧性的特征,获得了若干个充要条件.     

单位球上的混合模空间到Zygmund型空间的积分型算子

给出了单位球上从混合模空间H(p,q,φ)到Zygmund型空间的积分型算子P_g的有界性和紧性的特征,获得了几个充要条件.     

广义加权Bloch空间与QK(p,q)空间之间的复合算子

设φ是复平面上的单位圆盘D上的全纯自映射,0＜p＜∞,q＞-2,α＞0.本文给出广义加权Bloch空间与QK(p,q)空间之间的复合算子的有界性和紧性.     

Best constants for Hausdorf operators on n-dimensional product spaces

In this paper,we study certain Hausdorf operators in the high-dimensional product spaces.We obtain their power weighted boundedness from Lpto Lqand characterize the necessary and sufcient conditions for their boundedness on the power weighted Lpspaces.Moreover,in the case p=q,we obtain the sharp bound constants.     

A note on Besov-Morrey spaces and Triebel-Lizorkin-Morrey spaces

In the present paper, we obtain three independent results on the Besov-Morrey spaces and the Triebel-Lizorkin-Morrey spaces. That is, we are going to obtain the characterization of local means, the boundedness of pseudo-differential operators and the characterization of the Hardy-Morrey spaces. By using the maximal estimate and the molecular decomposition, we shall integrate and extend the known results on these spaces.     

Optimal behavior of weighted Hardy operators on rearrangement-invariant spaces

The behavior of certain weighted Hardy-type operators on rearrangement-invariant function spaces is thoroughly studied. Emphasis is put on the optimality of the obtained results. First, the optimal rearrangement-invariant function spaces guaranteeing the boundedness of the operators from/to a given rearrangement-invariant function space are described. Second, the optimal rearrangement-invariant function norms being sometimes complicated, the question of whether and how they can be simplified to more manageable expressions is addressed. Next, the relation between optimal rearrangement-invariant function spaces and interpolation spaces is investigated. Last, iterated weighted Hardy-type operators are also studied.     

Composition operators between Bergman and Hardy spaces

We study composition operators between weighted Bergman spaces. Certain growth conditions for generalized Nevanlinna counting functions of the inducing map are shown to be necessary and sufficient for such operators to be bounded or compact. Particular choices for the weights yield results on composition operators between the classical unweighted Bergman and Hardy spaces.

     

Adjoint for operators in Banach spaces

In this paper we show that a result of Gross and Kuelbs, used to study Gaussian measures on Banach spaces, makes it possible to construct an adjoint for operators on separable Banach spaces. This result is used to extend well-known theorems of von Neumann and Lax. We also partially solve an open problem on the existence of a Markushevich basis with unit norm and prove that all closed densely defined linear operators on a separable Banach space can be approximated by bounded operators. This last result extends a theorem of Kaufman for Hilbert spaces and allows us to define a new metric for closed densely defined linear operators on Banach spaces. As an application, we obtain a generalization of the Yosida approximator for semigroups of operators.

     

Morrey spaces and fractional integral operators

The present paper is devoted to the boundedness of fractional integral operators in Morrey spaces defined on quasimetric measure spaces. In particular, Sobolev, trace and weighted inequalities with power weights for potential operators are established. In the case when measure satisfies the doubling condition the derived conditions are simultaneously necessary and sufficient for appropriate inequalities.     

Composition operators that improve integrability on weighted Bergman spaces

Composition operators between weighted Bergman spaces with a smaller exponent in the target space are studied. An integrability condition on a generalized Nevanlinna counting function of the inducing map is shown to characterize both compactness and boundedness of such an operator. Composition operators mapping into the Hardy spaces are included by making particular choices for the weights.

     

Completeness of quasi-normed symmetric operator spaces

We show that (generalized) Calkin correspondence between quasi-normed symmetric sequence spaces and symmetrically quasi-normed ideals of compact operators on an infinite-dimensional Hilbert space preserves completeness. We also establish a semifinite version of this result.     

Embedding of function spaces of variable order of differentiation in function spaces of variable order of integration

The paper deals with embeddings of function spaces of variable order of differentiation in function spaces of variable order of integration. Here the function spaces of variable order of differentiation are defined by means of pseudodifferential operators.     

Composition operators on weighted Dirichlet spaces

We characterize bounded and compact composition operators on weighted Dirichlet spaces. The method involves integral averages of the determining function for the operator, and the connection between composition operators on Dirichlet spaces and Toeplitz operators on Bergman spaces. We also present several examples and counter-examples that point out the borderlines of the result and its connections to other themes.