Commuting dual Toeplitz operators on weighted Bergman spaces of the unit ball

In this paper, we study the commutativity of dual Toeplitz operators on weighted Bergman spaces of the unit ball. We obtain the necessary and sufficient conditions for the commutativity, essential commutativity and essential semi-commutativity of dual Toeplitz operator on the weighted Bergman spaces of the unit ball.     

Hankel and Toeplitz type operators on the unit disk

Let D be the unit disk in the complex plane with the weighted measure dμβ(z) = (β+1)--π(1-|z|2)βdm(z)(β＞-1). Then L2(D,dμβ(z)) = ∞k=0(Aβk Aβk) is the orthogonal direct sum decomposition.In this paper, we define the Hankel and Toeplitz type operators, and study the boundedness, compactness and Sp-criteria for them.     

Hankel and Toeplitz operators on Dirichlet spaces

In this paper we study Hankel and Toeplitz operators on Dirichlet type spaces D. We obtain necessary and sufficient condition on the symbols for these operators to be bounded and to belong to the Schatten ideal S^p for certain and p.     

Bounded Toeplitz products on the weighted Bergman spaces of the unit ball

Let p>1 and let q denote the number such that (1/p)+(1/q)=1. We give a necessary condition for the product of Toeplitz operators to be bounded on the weighted Bergman space of the unit ball (α>−1), where and , as well as a sufficient condition for to be bounded on . We use techniques different from those in [K. Stroethoff, D. Zheng, Bounded Toeplitz products on Bergman spaces of the unit ball, J. Math. Anal. Appl. 325 (2007) 114-129], in which the case p=2 was proved.     

Hankel and Toeplitz operators in hardy spaces

In this paper one considers some general theorems of the theory of Hankel and Toeplitz operators in spaces of analytic functions. Under natural restrictions on the spaces X, it is shown that the symbols of the Toeplitz operators, acting in X, are bounded. One describes completely the symbols of the Hankel and Toeplitz operators, acting from H^p into ¯H_q (into H^q) for 0 < p, q < .Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 141, pp. 165–175, 1985.The author expresses his gratitude to A. L. Vol'berg and S. V. Kislyakov for useful discussions.     

Toeplitz operators on harmonic Bergman spaces

We study Toeplitz operators on the harmonic Bergman spaceb ^p (B), whereB is the open unit ball inR ⁿ(n2), for 1<p. We give characterizations for the Toeplitz operators with positive symbols to be bounded, compact, and in Schatten classes. We also obtain a compactness criteria for the Toeplitz operators with continuous symbols.     

Weighted reproducing kernels and Toeplitz operators on harmonic Bergman spaces on the real ball

For the standard weighted Bergman spaces on the complex unit ball, the Berezin transform of a bounded continuous function tends to this function pointwise as the weight parameter tends to infinity. We show that this remains valid also in the context of harmonic Bergman spaces on the real unit ball of any dimension. This generalizes the recent result of C. Liu for the unit disc, as well as the original assertion concerning the holomorphic case. Along the way, we also obtain a formula for the corresponding weighted harmonic Bergman kernels.

     

Hankel operators on the weighted Bergman spaces with exponential type weights

Let denote the closed subspace of consisting of analytic functions in the unit disk . For certain class of subharmonic , the Hankel operatorH _b on with symbol is studied. Criteria for boundedness and compactness of such kind of Hankel operators are presented.R. Rochberg's research was partially supported by a grant from the National Science Foundation.     

Toeplitz operators on weighted Bergman spaces

In [2], Axler, Conway and McDonald, discuss the essential spectrum of Toeplitz operator, with continuous symbol, on the unweighted Bergman space. This paper extends their results to the weighted Bergman space, where the weight and its logarithm are assumed to be locally integrable.This paper represents part of the author's Ph.D. thesis, written at Indiana University under the direction of Professor John B. Conway.     

Compact Hankel operators on harmonic Bergman spaces

We study Hankel operators on the harmonic Bergman spaceb ²(B), whereB is the open unit ball inR ⁿ,n2. We show that iff is in then the Hankel operator with symbolf is compact. For the proof we have to extend the definition of Hankel operators to the spacesb ^p(B), 1<p<, and use an interpolation theorem. We also use the explicit formula for the orthogonal projection ofL ²(B, dV) ontob ²(B). This result implies that the commutator and semi-commutator of Toeplitz operators with symbols in are compact.     

Toeplitz operators with BMO symbols on the weighted Bergman space of the unit ball

In this paper we prove that the boundedness and compactness of Toeplitz operator with a BMO _α ¹ symbol on the weighted Bergman space A _α ²(B _n ) of the unit ball is completely determined by the behavior of its Berezin transform, where α > −1 and n ≥ 1.     

Toeplitz and Hankel type operators on the upper half-plane

An orthogonal decomposition of admissible wavelets is constructed via the Laguerre polynomials, it turns to give a complete decomposition of the space of square integrable functions on the upper half-plane with the measurey dxdy. The first subspace is just the weighted Bergman (or Dzhrbashyan) space. Three types of Ha-plitz operators are defined, they are the generalization of classical Toeplitz, small and big Hankel operators respectively. Their boundedness, compactness and Schatten-von Neumann properties are studied.Research was supported by the National Natural Science Foundation of China.     

Weighted composition operators from weighted Bergman spaces to weighted-type spaces on the unit ball

We calculate the operator norm of the weighted composition operator from a weighted Bergman space to a weighted-type space on the unit ball of Cⁿ. We also characterize the compactness of the operator.     

Toeplitz operators on weighted Hardy and Besov spaces

We obtain estimates of the norm of Toeplitz operators on weighted Hardy and Besov spaces. As an application we give characterizations of some spaces of pointwise multipliers.     

On generalized Toeplitz and little Hankel operators on Bergman spaces

We find a concrete integral formula for the class of generalized Toeplitz operators \(T_a\) in Bergman spaces \(A^p\), \(1<p<\infty \), studied in an earlier work by the authors. The result is extended to little Hankel operators. We give an example of an \(L^2\)-symbol a such that \(T_{|a|} \) fails to be bounded in \(A^2\), although \(T_a : A^2 \rightarrow A^2\) is seen to be bounded by using the generalized definition. We also confirm that the generalized definition coincides with the classical one whenever the latter makes sense.