共查询到20条相似文献,搜索用时 15 毫秒
1.
讨论C~m上Fock空间之正交补空间上以平方可积函数为符号的对偶Toeplitz算子,并给出其有界性与紧性的等价判别条件. 相似文献
2.
吴焕春 《数学的实践与认识》2008,38(23)
Fock空间是由整函数组成的具有再生核的Hilbert空间.Fock空间上的乘法算子的定义域不是整个Fock空间,它在Fock空间上是稠定的.研究了Fock空间上的乘法算子的性质,对其值域进行了刻画,并得出了乘法算子作用在Fock空间的拟不变子空间上值域余一维的充要条件. 相似文献
3.
We study Toeplitz operators on the Fock space with positive measures as symbols. Main results include characterizations of
Fock–Carleson measures, bounded Toeplitz operators, compact Toeplitz operators, and Toeplitz operators in the Schatten p-classes. 相似文献
4.
5.
Compactness of Product Operators on the Bergman Space 总被引:2,自引:0,他引:2
Mao Fa WANG Pei De LIU 《数学学报(英文版)》2005,21(4):723-732
In this paper, we study the compactness of the product of a composition operator with another one's adjoint on the Bergman space. Some necessary and sufficient conditions for such operators to be compact are given. 相似文献
6.
7.
In the present work, necessary and sufficient conditions are given in terms of a nonnegative Borel measure which ensure the boundedness and compactness of operators with power-logarithmic kernels from L
p
(0, a) to L
p
(0, a) (or to L
q
(0, a)), where 0 < a < , 1 < p, q < , > 1/p and 0. 相似文献
8.
Let > 0. The operator of the form
is considered, where the real weight function v(x) is locallyintegrable on R+ := (0, ). In case v(x) = 1 the operator coincideswith the RiemannLiouville fractional integral, Lp Lqestimates of which with power weights are well known. This workgives Lp Lqboundedness and compactness criteria for the operatorT in the case 0 < p, q < , p > max(1/, 1). 相似文献
9.
E. A. Gallardo-Gutiérrez R. Kumar J. R. Partington 《Integral Equations and Operator Theory》2010,67(4):467-479
The boundedness and compactness of weighted composition operators on the Hardy space H2{{\mathcal H}^2} of the unit disc is analysed. Particular reference is made to the case when the self-map of the disc is an inner function.
Schatten-class membership is also considered; as a result, stronger forms of the two main results of a recent paper of Gunatillake
are derived. Finally, weighted composition operators on weighted Bergman spaces
A2a(\mathbbD){\mathcal{A}^2_\alpha(\mathbb{D})} are considered, and the results of Harper and Smith, linking their properties to those of Carleson embeddings, are extended
to this situation. 相似文献
10.
本文讨论了Fock空间上以径向函数和拟齐次函数为符号的Toeplitz算子的代数性质,给出了两个以径向函数为符号的Toeplitz算子的积仍为Toeplitz算子的充分必要条件,并且研究了以拟齐次函数为符号的Toeplitz算子的交换性. 相似文献
11.
This paper studies a class of weighted composition operators and their spectrum on the Fock space.As an application,bounded self-adjoint,a class of complex symmetric weighted composition operators on the Fock space are characterized. 相似文献
12.
Yu. I. Karlovich 《Integral Equations and Operator Theory》2012,73(2):217-254
Applying the boundedness on weighted Lebesgue spaces of the maximal singular integral operator S * related to the Carleson?CHunt theorem on almost everywhere convergence, we study the boundedness and compactness of pseudodifferential operators a(x, D) with non-regular symbols in ${L^\infty(\mathbb{R}, V(\mathbb{R})), PC(\overline{\mathbb{R}}, V(\mathbb{R}))}$ and ${\Lambda_\gamma(\mathbb{R}, V_d(\mathbb{R}))}$ on the weighted Lebesgue spaces ${L^p(\mathbb{R},w)}$ , with 1?< p <? ?? and ${w\in A_p(\mathbb{R})}$ . The Banach algebras ${L^\infty(\mathbb{R}, V(\mathbb{R}))}$ and ${PC(\overline{\mathbb{R}}, V(\mathbb{R}))}$ consist, respectively, of all bounded measurable or piecewise continuous ${V(\mathbb{R})}$ -valued functions on ${\mathbb{R}}$ where ${V(\mathbb{R})}$ is the Banach algebra of all functions on ${\mathbb{R}}$ of bounded total variation, and the Banach algebra ${\Lambda_\gamma(\mathbb{R}, V_d(\mathbb{R}))}$ consists of all Lipschitz ${V_d(\mathbb{R})}$ -valued functions of exponent ${\gamma \in (0,1]}$ on ${\mathbb{R}}$ where ${V_d(\mathbb{R})}$ is the Banach algebra of all functions on ${\mathbb{R}}$ of bounded variation on dyadic shells. Finally, for the Banach algebra ${\mathfrak{A}_{p,w}}$ generated by all pseudodifferential operators a(x, D) with symbols ${a(x, \lambda) \in PC(\overline{\mathbb{R}}, V(\mathbb{R}))}$ on the space ${L^p(\mathbb{R}, w)}$ , we construct a non-commutative Fredholm symbol calculus and give a Fredholm criterion for the operators ${A \in \mathfrak{A}_{p,w}}$ . 相似文献
13.
In this paper we show that the C*-algebra generated by radial Toeplitz operators with \(L_{\infty }\)-symbols acting on the Fock space is isometrically isomorphic to the C*-algebra of bounded sequences uniformly continuous with respect to the square-root-metric \(\rho (j,k)=|\sqrt{j}-\sqrt{k}\,|\). More precisely, we prove that the sequences of eigenvalues of radial Toeplitz operators form a dense subset of the latter C*-algebra of sequences. 相似文献
14.
In this paper, we study Toeplitz operators T μ from one Fock space \({F^{p}_{\alpha}}\) to another \({F^{q}_{\alpha}}\) for 1 < p, q < ∞ with positive Borel measures μ as symbols. We characterize the boundedness (and compactness) of \({T_\mu: F^{p}_{\alpha} \to F^{q}_{\alpha}}\) in terms of the averaging function \({\widehat{\mu}_r}\) and the t-Berezin transform \({\widetilde{\mu}_t}\) respectively. Quite differently from the Bergman space case, we show that T μ is bounded (or compact) from \({F^{p}_{\alpha}}\) to \({F^{q}_{\alpha}}\) for some p ≤ q if and only if T μ is bounded (or compact) from \({F^{p}_{\alpha}}\) to \({F^{q}_{\alpha}}\) for all p ≤ q. In order to prove our main results on T μ , we introduce and characterize (vanishing) (p, q)-Fock Carleson measures on C n . 相似文献
15.
Cai Shi WANG Zhi Yuan HUANG Xiang Jun WANG 《数学学报(英文版)》2005,21(4):787-796
In this paper we first introduce and investigate some special classes of nonlinear maps and get several useful results. Then, by using these results, we obtain analytic criteria for checking whether or not an operator defined only on the exponential vectors of a symmetric Fock space becomes a Hilbert-Schmidt operator on the whole space. Additionally, as an application, we also get an analytic criterion for Hilbert-Schmidt operators on a Gaussian probability space through the Wiener-Ito-Segal isomorphism. 相似文献
16.
Boundedness of Toeplitz Type Operators Associated to Fractional and Pseudo-Differential Operators on Orlicz Space 下载免费PDF全文
Dazhao Chen 《偏微分方程(英文版)》2021,34(4):297-312
In this paper, the boundedness from Lebesgue space to Orlicz space of certain Toeplitz type operator related to the fractional and pseudo-differential operators
is obtained. 相似文献
17.
Boundedness of Multilinear Operators in Herz-type Hardy Space 总被引:1,自引:0,他引:1
Let κ∈ℕ. We prove that the multilinear operators of finite sums of products of singular integrals on ℝn are bounded from HK
α1,p1
q1
(ℝn) ×···×HK
αk,pk
qk
(ℝn) into HK
α,p
q
(ℝn) if they have vanishing moments up to a certain order dictated by the target spaces. These conditions on vanishing moments
satisfied by the multilinear operators are also necessary when αj≥ 0 and the singular integrals considered here include the Calderón-Zygmund singular integrals and the fractional integrals
of any orders.
Received September 6, 1999, Revised November 17, 1999, Accepted December 9, 1999 相似文献
18.
本文证明了Rn上奇异积分乘积之有限和的多线性算子是从HKq1α1,p1(Rn)×… ×HKqkαk,pk(Rn)到HKqα,p(Rn)有界的,如果它满足由目标空间所确定的直到一定阶的消失矩条件.这些多线性算子所满足的消失矩条件,当αj≥0时也是必要的.而且,这里所考虑的奇异积分包括Calderon-Zygmund奇异积分及任意阶的分数次积分. 相似文献
19.
《数学研究及应用》2016,(3)
This paper shows that a bounded invertible weighted composition operator on the Fock space of C~N is nonzero multiples of a unitary operator, which is an addition to the recent result on invertible weighted composition operator on the Fock space of C~N and an extension to the corresponding result on the Fock space of C. 相似文献
20.
研究了一类次线性算子在加权Herz空间.Knq(1-1/q),p(ω1;ω2)上的有界性. 相似文献