共查询到19条相似文献,搜索用时 140 毫秒
1.
与调和Bergman 空间相对应, 本文研究重调和Hardy 空间h2(D2) 上的Toeplitz 算子. 本文发现, h2(D2) 上的Toeplitz 算子与经典的Hardy 空间、Bergman 空间及调和Bergman 空间上的Toeplitz算子的性质都有很大的差异. 例如解析Toeplitz 算子可以不是半可换及可交换的. 即使半可换, 其中任何一个符号可以不为常数; 即使可交换, 两个符号的非平凡线性组合也不一定是常数. 本文得到了h2(D2) 上两个解析Toeplitz 算子半可换和可换的充分必要条件. 相似文献
2.
本文给出加权Bergman空间Ap(φ)上具有界调和符号的Toeplitz算子的半换位子为零或为紧算子的一些充要条件. 相似文献
3.
4.
本文研究了单位圆盘D 的Dirichlet 空间上Toeplitz 算子和小Hankel 算子. 利用Berezin 型变换讨论了Toeplitz 算子的不变子空间问题, 具有Berezin 型符号的Toeplitz 算子的渐进可乘性以及Toeplitz 算子的Riccati 方程的可解性. 应用Berezin 变换得到了Toeplitz 算子和小Hankel 算子可逆的充分条件. 此外, 还利用Hankel 算子和Berezin 变换刻画了算子2Tuv-TuTv-TvTu 的紧性, 其中函数u,v ∈ L2,1. 相似文献
5.
《数学物理学报(A辑)》2015,(5)
该文讨论了调和Dirichlet空间D_h~1上Toeplitz与Hankel算子的有界性、紧性与Fredholm性质,计算了Toeplitz算子的Fredholm指标. 相似文献
6.
7.
该文在Cn中单位球上讨论了Zygmund 型空间(小Zygmund 型空间)之间的加权Cesàro 算子Tg 的有界性和紧性特征, 得到了以下的结果: (1) Tg 是Zp 到Zq的有界算子或紧算子的充要条件; (2) Tg 是 Zp0 到Zq0 的有界算子或紧算子的充要条件. 相似文献
8.
9.
本文给出Cn中单位球上的带权的Bergman空间上具L∞-符号的Toeplitz算子或Hankel算子为紧的充要条件。 相似文献
10.
11.
Bastos M. A.; Karlovich Yu. I.; Silbermann B. 《Proceedings London Mathematical Society》2004,89(3):697-737
We develop the Fredholm theory for Toeplitz operators, withsymbols in the C*-algebra D = [SO, SAP]n, n generated by allslowly oscillating (SO) and semi-almost periodic (SAP) n x nmatrix functions, on the Hardy spaces (with 1 < p < ) over the upper half-plane.Using limit operator techniques, we get necessary Fredholm conditionsfor any operator in the Banach algebra alg(S, D) of singularintegral operators with coefficients in D on the space [Lp (R)]n.Applying the AllanDouglas local principle and the theoryof Toeplitz operators with SAP matrix symbols, we also establishFredholm criteria for Toeplitz operators with matrix symbolsg D on the space . An index formula for Fredholm Toeplitz operators with matrix symbolsin D is obtained on the basis of an appropriate approximationof slowly oscillating components of the symbols. 2000 MathematicsSubject Classification 47B35 (primary), 47A53 (secondary). 相似文献
12.
Xuejun Zhang 《Journal of Mathematical Analysis and Applications》2003,285(2):376-386
In the paper, we will discuss the pointwise multipliers from Dirichlet type space Dp to Bloch type space βq on the unit ball of Cn. The multiplier spaces M(Dp,βq) are fully characterized for all p, q. 相似文献
13.
Harold Widom proved in 1966 that the spectrum of a Toeplitz operator T(a) acting on the Hardy space
Hp(\mathbbT)H^p({\mathbb{T}}) over the unit circle
\mathbbT{\mathbb{T}} is a connected subset of the complex plane for every bounded measurable symbol a and 1 < p < ∞. In 1972, Ronald Douglas established the connectedness of the essential spectrum of T(a) on
H2(\mathbbT)H^2({\mathbb{T}}). We show that, as was suspected, these results remain valid in the setting of Hardy spaces Hp(Γ,w), 1 < p < ∞, with general Muckenhoupt weights w over arbitrary Carleson curves Γ. 相似文献
14.
Gregory Verchota 《Journal of Functional Analysis》1984,59(3):572-611
For D, a bounded Lipschitz domain in Rn, n ? 2, the classical layer potentials for Laplace's equation are shown to be invertible operators on L2(?D) and various subspaces of L2(?D). For 1 < p ? 2 and data in Lp(?D) with first derivatives in Lp(?D) it is shown that there exists a unique harmonic function, u, that solves the Dirichlet problem for the given data and such that the nontangential maximal function of ▽u is in Lp(?D). When n = 2 the question of the invertibility of the layer potentials on every Lp(?D), 1 < p < ∞, is answered. 相似文献
15.
Nazih S. Faour 《Rendiconti del Circolo Matematico di Palermo》1986,35(2):221-232
Let ? be an element in \(H^\infty (D) + C(\overline D )\) such that ?* is locally sectorial. In this paper it is shown that the Toeplitz operator defined on the Bergman spaceA 2 (D) is Fredholm. Also, it is proved that ifS is an operator onA 2(D) which commutes with the Toeplitz operatorT ? whose symbol ? is a finite Blaschke product, thenS H ∞ (D) is contained inH ∞ (D). Moreover, some spectral properties of Toeplitz operators are discussed, and it is shown that the spectrum of a class of Toeplitz operators defined on the Bergman spaceA 2 (D), is not connected. 相似文献
16.
有界连通区域上Dirichlet空间及其算子 总被引:1,自引:0,他引:1
本文主要讨论了有界连通区域Dirichlet空间上Toeplitz算子的Fredholm性质,计算了符号在C1中的Toeplitz算子的本性谱和Fredholm指标. 相似文献
17.
A Toeplitz operator TfT_\phi with symbol f\phi in
L¥(\mathbbD)L^{\infty}({\mathbb{D}}) on the Bergman space
A2(\mathbbD)A^{2}({\mathbb{D}}), where
\mathbbD\mathbb{D} denotes the open unit disc, is radial if f(z) = f(|z|)\phi(z) = \phi(|z|) a.e. on
\mathbbD\mathbb{D}. In this paper, we consider the numerical ranges of such operators. It is shown that all finite line segments, convex hulls
of analytic images of
\mathbbD\mathbb{D} and closed convex polygonal regions in the plane are the numerical ranges of radial Toeplitz operators. On the other hand,
Toeplitz operators TfT_\phi with f\phi harmonic on
\mathbbD\mathbb{D} and continuous on
[`(\mathbbD)]{\overline{\mathbb{D}}} and radial Toeplitz operators are convexoid, but certain compact quasinilpotent Toeplitz operators are not. 相似文献
18.
该文研究了Lp(Ω,∑,μ; Lq(X, A,ν)) (2≤q
p (Ω,∑,μ; Lq(X,A,ν))(1
相似文献
19.
Shi Jihuai 《数学学报(英文版)》1994,10(1):11-18
In this paper, the spaceD
p(Ω) of functions holomorphic on bounded symmetric domain ofC
n is defined. We prove thatH
p(Ω)⊂D
p(Ω) if 0<p≤2, andD
p(Ω)⊂H
p(Ω) ifp≥2, and both the inclusions are proper. Further, we find that some theorems onH
p(Ω) can be extended to a wider classD
p(Ω) for 0<p≤2. 相似文献