从$A^{p}_{\alpha}$到$A^{\infty}(\varphi)$的加权复合算子

设$u \in H(D), \ \phi$为$D$上的解析自映射,定义$H(D)$上的加权复合算子为$u C_{\phi}(f)=$$uf\circ\phi$, \ $f\in H(D)$.本文得到了从$A^{p}_{\alpha}$到$A^{\infty}(\varphi)\ (A_{0}^{\infty}(\varphi))$的加权复合算子$u C_{\phi}$的有界性和紧性的充要条件.     

从β0到E(p,q)和E0(p,q)空间的复合算子

设ψ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Cψ:Cψ(f)=foψ.我们利用从β0到E(p,q)和E0(p,q)空间的复合算子研究了空间E(p,q)和E0(p,q),给出了-个新的特征.     

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．     

$\mathbb{C}^{n}$中$\mu$-Bergman空间的刻画和微分复合算子

设$p>0$, $\mu$和$\mu_{1}$是$[0,1)$上的正规函数. 本文首先给出了$\mathbb{C}^{n}$中单位球上$\mu$-Bergman空间$A^{p}(\mu)$的几种等价刻画; 然后 分别刻画了$A^{p}(\mu)$到$A^{p}(\mu_{1})$的 微分复合算子$D_{\varphi}$为有界算子以及紧算子的充要条件, 同时给出了当$p>1$时$D_{\varphi}$为 $A^{p}(\mu)$到$A^{p}(\mu_{1})$上紧算子的一种简捷充分条件和必要条件.     

Zygmund 空间到 Bloch 空间上径向导数算子与积分型算子的乘积

设$H(\mathbb{B})$为单位球上全纯函数类,研究了单位球上 Zygmund 空间到 Bloch 空间上径向导数算子$\Re$与积分型算子$I_\varphi^g$乘积的有界性和紧性, 这里 $$ I_\varphi^g f(z)=\int_0^1 \Re f(\varphi(tz))g(tz)\frac{{\rm d}t}{t},\quad z\in\mathbb{B}, $$ 其中$g\in H(\mathbb{B}),\ g(0)=0$, $\varphi$ 是$\mathbb{B}$上全纯自映射.     

单位球上F(p,q,s)空间到Bloch型空间的复合算子

该文分别给出了单位球B上空间F(p, q, s)到空间β^α之复合算子C_{varphi}为有界算子和紧算子的充要条件.同时作为推论获得了Bloch型空间的相应结果.     

{C}^n$中单位球上Bergman型空间的一种积分算子

设$\omega_1,\omega_2$为正规函数, $\varphi$是$B_n$ 上的全纯自映射,$ g\in H(B_n)$ 满足 $g(0)=0$. 对所有的$0相似文献   

Cn中空间F(p,q,s)到βq+n+1/p的复合算子

对一切P＞0,s≥0和q＞q＞max{-n-1,-s-1},给出了单位球上一般函数空间F(p,q,s)到Bloch型空间βq+n+1/p之复合算子Cψ有界和紧的充要条件,并给出了几个推论.     

由$q$-积分算子定义的某些亚纯函数类的Fekete-Szeg\"{o}问题

本文首先引入满足如下条件$$-\frac{qzD_{q}f(z)}{f(z)}\prec \varphi (z)$$和$$\frac{-(1-\frac{\alpha }{q})qzD_{q}f(z)+\alpha qzD_{q}[zD_{q}f(z)]}{(1-\frac{\alpha}{q})f(z)-\alpha zD_{q}f(z)}\prec \varphi (z)~(\alpha \in\mathbb{C}\backslash (0,1],\ 0相似文献   

映入E0(p,q)的紧复合算子

应用复合算子研究E₀（p,q）空间,当p=2时,它就是Q_q,0,当P>0且q>1时,它就是小 Bloch空间B₀.讨论了复合算子的紧性并利用Carleson测度给出复合算子是紧的判别准则.     

从$\alpha$-Bloch空间到$Q_K$型空间的复合算子

Suppose φ is an analytic map of the unit disk D into itself, X is a Banach space of analytic functions on D. Define the composition operator Cφ： Cφf = f °φ, for all f ∈ X. In this paper, the boundedness and compactness of the composition operators from α-Bloch spaces into QK（p,q） and QK,0（p,q） spaces are discussed, where 0 〈 α 〈 ∞.     

Hardy-Orlicz 空间到 Bloch-Orlicz 型空间上的复合算子

Let φ be an analytic self-map of D. The composition operator C_φ is the operator defined on H(D) by C_φ(f) = f ? φ. In this paper, we investigate the boundedness and compactness of the composition operator C_φ from Hardy-Orlicz spaces to Bloch-Orlicz type spaces.     

$C(X)$上的开点与紧开拓扑

In this note we define a new topology on C(X),the set of all real-valued continuous functions on a Tychonoff space X.The new topology on C(X) is the topology having subbase open sets of both kinds:[f,C,ε[={g E C(X):|f(x)-g(x)| ε for every x∈C} and[U,r]~-={g∈C(X):g~(-1)(r)∩U≠φ},where f∈C(X),C∈KC(X)={nonempty compact subsets of X},ε 0,while U is an open subset of X and r∈R.The space C(X) equipped with the new topology T_(kh) which is stated above is denoted by C_(kh)(X).Denote X_0={x∈X:x is an isolated point of X} and X_c={x∈X:x has a compact neighborhood in X}.We show that if X is a Tychonoff space such that X_0=X_c,then the following statements are equivalent:(1) X_0 is G_δ-dense in X;(2) C_(kh)(X) is regular;(3) C_(kh)(X) is Tychonoff;(4) C_(kh)(X) is a topological group.We also show that if X is a Tychonoff space such that X_0=X_c and C_(kh)(X) is regular space with countable pseudocharacter,then X is σ-compact.If X is a metrizable hemicompact countable space,then C_(kh)(X) is first countable.     

${[\ell_p]}_{e.r}$ Euler-Riesz Difference Sequence Spaces

Başar and Braha [1], introduced the sequence spaces $\breve{\ell}_\infty$, $\breve{c}$ and $\breve{c}_0$ of Euler-Cesáro bounded, convergent and null difference sequences and studied their some properties. Then, in [2], we introduced the sequence spaces ${[\ell_\infty]}_{e.r}, {[c]}_{e.r}$ and ${[c_0]}_{e.r}$ of Euler-Riesz bounded, convergent and null difference sequences by using the composition of the Euler mean $E_1$ and Riesz mean $R_q$ with backward difference operator $\Delta$. The main purpose of this study is to introduce the sequence space ${[\ell_p]}_{e.r}$ of Euler-Riesz $p-$absolutely convergent series, where $1 \leq p <\infty$, difference sequences by using the composition of the Euler mean $E_1$ and Riesz mean $R_q$ with backward difference operator $\Delta$. Furthermore, the inclusion $\ell_p\subset{[\ell_p]}_{e.r}$ hold, the basis of the sequence space ${[\ell_p]}_{e.r}$ is constructed and $\alpha-$, $\beta-$ and $\gamma-$duals of the space are determined. Finally, the classes of matrix transformations from the ${[\ell_p]}_{e.r}$ Euler-Riesz difference sequence space to the spaces $\ell_\infty, c$ and $c_0$ are characterized. We devote the final section of the paper to examine some geometric properties of the space ${[\ell_p]}_{e.r}$.     

Weak type (p,q)‐inequalities for the Haar system and differentially subordinated martingales

For any $1\leq p,\,q<\infty$, we determine the optimal constant $C_{p,q}$ such that the following holds. If $(h_k)_{k\geq 0}$ is the Haar system on [0,1], then for any vectors a_k from a separable Hilbert space $\mathcal{H}$ and $\varepsilon_k\in \{-1,1\}$, $k=0,\,1,\,2,\ldots,$ we have This is generalized to the sharp weak‐type inequality where X, Y stand for $\mathcal{H}$‐valued martingales such that Y is differentially subordinate to X.     

Composition operators on Dirichlet-type spaces

The Dirichlet-type space ) is the Banach space of functions analytic in the unit disc with derivatives belonging to the Bergman space . Let be an analytic self-map of the disc and define for . The operator is bounded (respectively, compact) if and only if a related measure is Carleson (respectively, compact Carleson). If is bounded (or compact) on , then the same behavior holds on ) and on the weighted Dirichlet space . Compactness on implies that is compact on the Hardy spaces and the angular derivative exists nowhere on the unit circle. Conditions are given which, together with the angular derivative condition, imply compactness on the space . Inner functions which induce bounded composition operators on are discussed briefly.

     

从$Q_{k}(p,q)$空间到加权$\alpha-Bloch$空间的加权复合微分后置和前置算子

We study the boundedness and compactness of the weighted composition followed and proceeded by differentiation operators from Q_k（p,q）space to weighted α-Bloch space and little weighted α-Bloch space.Some necessary and sufficient conditions for the boundedness and compactness of these operators are given.     

Bounded composition operators with closed range on the Dirichlet space

For composition operators on spaces of analytic functions it is well known that norm estimates can be converted to Carleson measure estimates. The boundedness of the composition operator becomes equivalent to a Carleson measure inequality. The measure corresponding to a composition operator on the Dirichet space is , where is the cardinality of the preimage . The composition operator will have closed range if and only if the corresponding measure satisfies a ``reverse Carleson measure' theorem: for all . Assuming is bounded, a necessary condition for this inequality is a reverse of the Carleson condition: (C) for all Carleson squares . It has long been known that this is not sufficient for a completely general measure. Here we show that it is also not sufficient for the special measures . That is, we construct a function such that is bounded and satisfies (C) but the composition operator does not have closed range.