共查询到19条相似文献,搜索用时 78 毫秒
1.
Xiaofen LV 《数学年刊B辑(英文版)》2019,40(3):349-362
Given φ a subharmonic function on the complex plane C,with ?φdA being a doubling measure,the author studies Fock Carleson measures and some characterizations onμsuch that the induced positive Toeplitz operator T_μ is bounded or compact between the doubling Fock space F_φ~p and F_φ~∞ with 0p≤∞,where μ is a positive Borel measure on C. 相似文献
2.
Forα1,let dvαdenote the weighted Lebesgue measure on the bidisk andμa complex measure satisfying some Carleson-type conditions.In this paper,we show a sufcient and necessary condition for the Toeplitz operatorTαˉμto be bounded or compact on weighted Bergman spaceL1a(dvα). 相似文献
3.
In this paper, we mainly study the hyponormality of dual Toeplitz operators on the orthogonal complement of the harmonic Bergman space. First we show that the dual Toeplitz operator with the bounded symbol is hyponormal if and only if it is normal. Then we obtain a necessary and sufficient condition for the dual Toeplitz operator ■ with the symbol ■ to be hyponormal. Finally, we show that the rank of the commutator of two dual Toeplitz operators must be an even number if the commutator has a fin... 相似文献
4.
In this paper,we prove that the necessary and sufficient condition for a Toeplitz operator Tu on the Dirichlet space to be hyponormal is that the symbol u is constant for the case that the projection of u in the Dirichlet space is a polynomial and for the case that u is a class of special symbols,respectively.We also prove that a Toeplitz operator with harmonic polynomial symbol on the harmonic Dirichlet space is hyponormal if and only if its symbol is constant. 相似文献
5.
It is proved that if is a nonconstant bounded analytic function on the unit ball B n and continuous on S n in C n , and ψ is a bounded measurable function on S n such that T * and T ψ commute, then ψ is the boundary value of an analytic function on B n . In addition, the commutants of two Toeplitz operators are also discussed. 相似文献
6.
Let Ω be the unit ban or the polydisk of C^n and La^2 (Ω) the Bergman space. In this paper we prove that if S is a finite sum of finite products of Toeplitz operators on La^2 (Ω), then S is compact if and only if the Berezin transform S↑-(z) of S tends to zero as z→эΩ. 相似文献
7.
Li Xin CHENG Yan Mei TENG 《数学学报(英文版)》2007,23(6):1063-1066
To guarantee every real-valued convex function bounded above on a set is continuous, how "thick" should the set be? For a symmetric set A in a Banach space E,the answer of this paper is: Every real-valued convex function bounded above on A is continuous on E if and only if the following two conditions hold: i) spanA has finite co-dimentions and ii) coA has nonempty relative interior. This paper also shows that a subset A C E satisfying every real-valued convex function bounded above on A is continuous on E if (and only if) every real-valued linear functional bounded above on A is continuous on E, which is also equivalent to that every real-valued convex function bounded on A is continuous on E. 相似文献
8.
In this paper we investigate some algebra properties of dual Toeplitz operators on the orthogonal complement of the Dirichlet space in the Sobolev space. We completely characterize commuting dual Toeplitz operators with harmonic symbols, and show that a dual Toeplitz operator commutes with a nonconstant analytic dual Toeplitz operator if and only if its symbol is analytic. We also obtain the sufficient and necessary conditions on the harmonic symbols for SφSφψ= Sφψ. 相似文献
9.
Jin Chuan HOU Xiu Ling ZHANG 《数学学报(英文版)》2006,22(1):179-186
Let X be an infinite-dimensional complex Banach space and denote by B(X) the algebra of all bounded linear operators acting on X. It is shown that a surjective additive map Φ from B(X) onto itself preserves similarity in both directions if and only if there exist a scalar c, a bounded invertible linear or conjugate linear operator A and a similarity invariant additive functional ψ on B(X) such that either Φ(T) = cATA^-1 + ψ(T)I for all T, or Φ(T) = cAT*A^-1 + ψ(T)I for all T. In the case where X has infinite multiplicity, in particular, when X is an infinite-dimensional Hilbert space, the above similarity invariant additive functional ψ is always zero. 相似文献
10.
Guang Fu CAO Xiao Feng WANG 《数学学报(英文版)》2007,23(5):925-934
In the present paper, a problem of Ioana Mihaila is negatively answered on the invertibility of composition operators on Riemann surfaces, and it is proved that the composition operator Cp is Predholm if and only if it is invertible if and only if p is invertible for some special cases. In addition, the Toeplitz operators on ∧1 2, a(M) for Riemann surface M are defined and some properties of these operators are discussed. 相似文献
11.
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
12.
本文讨论了实单位球上的平均有界振动M—调和函数的Carleson测度特征,证明了Mobius不变调和函数f(x)属于BMOH或VMOH当且仅当dμ(x)=(1-|x|~2)|f(x)|~2dv(x)是Carleson测度或紧Carleson测度。 相似文献
13.
Eun Sun Choi 《Czechoslovak Mathematical Journal》2008,58(1):93-111
We study Toeplitz operators between the pluriharmonic Bergman spaces for positive symbols on the ball. We give characterizations
of bounded and compact Toeplitz operators taking a pluriharmonic Bergman space b
p
into another b
q
for 1 < p, q < ∞ in terms of certain Carleson and vanishing Carleson measures.
This research was supported by KOSEF (R01-2003-000-10243-0) and Korea University Grant. 相似文献
14.
We define Toeplitz operators on all Dirichlet spaces on the unit ball of
and develop their basic properties. We characterize bounded, compact, and Schatten-class Toeplitz operators with positive
symbols in terms of Carleson measures and Berezin transforms. Our results naturally extend those known for weighted Bergman
spaces, a special case applies to the Arveson space, and we recover the classical Hardy-space Toeplitz operators in a limiting
case; thus we unify the theory of Toeplitz operators on all these spaces. We apply our operators to a characterization of
bounded, compact, and Schatten-class weighted composition operators on weighted Bergman spaces of the ball. We lastly investigate
some connections between Toeplitz and shift operators.
The research of the second author is partially supported by a Fulbright grant. 相似文献
15.
加权Bergman空间上的Carleson测度与复合算子 总被引:2,自引:0,他引:2
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。 相似文献
16.
Shiying Zhao 《Arkiv f?r Matematik》1992,30(1-2):345-365
In this paper, we prove a good-λ inequality between the nontangential maximal function and the square area integral of a subharmonic functionu in a bounded NTA domainD inR n . We achieve this by showing that a weighted Riesz measure ofu is a Carleson measure, with the Carleson norm bounded by a constant independent ofu. As consequences of the good-λ inequality, we obtain McConnell-Uchiyama's inequality and an analogue of Murai-Uchiyama's inequality for subharmonic functions inD. 相似文献
17.
Shiying Zhao 《Arkiv f?r Matematik》1992,30(1):345-365
In this paper, we prove a good-λ inequality between the nontangential maximal function and the square area integral of a subharmonic
functionu in a bounded NTA domainD inR
n
. We achieve this by showing that a weighted Riesz measure ofu is a Carleson measure, with the Carleson norm bounded by a constant independent ofu. As consequences of the good-λ inequality, we obtain McConnell-Uchiyama's inequality and an analogue of Murai-Uchiyama's
inequality for subharmonic functions inD. 相似文献
18.
Completely J — positive linear systems of finite order are introduced as a generalization of completely symmetric linear systems. To any completely J — positive linear system of finite order there is associated a defining measure with respect to which the transfer function has a certain integral representation. It is proved that these systems are asymptotically stable. The observability and reachability operators obey a certain duality rule and the number of negative squares of the Hankel operator is estimated. The Hankel operator is bounded if and only if a certain measure associated with the defining measure is of Carleson type. We prove that a real symmetric operator valued function which is analytic outside the unit disk has a realization with a completely J — symmetric linear space which is reachable, observable and parbalanced. Uniqueness and spectral minimality of the completely J — symmetric realizations are discussed. 相似文献