Hankel operators on the Bergman spaces of strongly pseudoconvex domains

We characterize functions fL ²(D) such that the Hankel operators H_f are, respectively, bounded and compact on the Bergman spaces of bounded strongly pseudoconvex domains.Research partially supported by a grant of the National Science Foundation.     

Continuity of Bergman and Szegö projections on weighted-sup function spaces on pseudoconvex domains

We study regularity of Bergman and Szeg? projections on Sobolev type weighted-sup spaces. The paper covers the case of strongly pseudoconvex domains with C⁴ boundary and, partially, domains of finite type in the sense of D’Angelo. Received: 6 October 2005     

The essential norm of Hankel operator on the Bergman spaces of strongly pseudoconvex domains

Let D be a bounded strongly pseudoconvex domain with smooth boundary in Cⁿ and let fL²(D). For the Hankel operator H_f on the Bergman space A²(D), it is shown that the essential norm of H_f in L²(D) is comparable to the distance norm from H_f to compact Hankel operators. The result extends the previous corresponding version in the disc proved by Lin and Rochberg in Integ.Equat.Oper.Theory 361–372,17 (1993).     

An invariant subspace problem forp=1 Bergman spaces on slit domains

In this paper, we characterize thez-invariant subspaces that lie between the Bergman spacesA ¹ (G) andA ¹ (G/K), whereG is a bounded region in the complex plane andK is a compact subset of a simple arc of classC ¹.     

Bergman spaces with exponential weights

In this paper we introduce a kind of Bergman space $A_{\phi }^p$ on the unit disk D with exponential weights, which cover those defined by Borichev et al. (2007) [6]. We obtain upper and lower bound estimates on the Bergman kernel. As an application, we discuss the Bergman projection and duality.     

加权Bergman空间上的Carleson测度与Toeplitz算子

探讨加权Bergman空间Ap()上的Carleson型测度和具有非负测度符号的Toeplitz算子,给出Carleson测度或消没Carleson测度的若干等价描述并用Carleson测度的方法刻画了Toeplitz算子是有界的或紧致的充要条件.     

The Density Problem for Self–Commutators of Unbounded Bergman Operators

We give two sufficient conditions for the self–commutator of an unbounded Bergman operator to be densely defined. In conjunction with known results this leads to a strong Berger–Shaw type theorem for unbounded Bergman operators. Finally we present results regarding the density problem for unbounded sets in the plane of infinite area.     

Shift invariant spaces inL 2

If is a complex, separable Hilbert space, letL ² () denote theL ²-space of functions defined on the unit circle and having values in . The bilateral shift onL ²() is the operator (U f)()=f(). A Hilbert spaceH iscontractively contained in the Hilbert spaceK ifHK and the inclusion mapH–K is a contraction. We describe the structure of those Hilbert spaces, contractively contained inL ²(), that are carried into themselves contractively byU . We also do this for the subcase of those spaces which are carried into themselves unitarily byU .     

On the Bergman metric of pseudoconvex domains in a complex projective space

We prove a localization principle of the Bergman kernel form and metric for pseudoconvex domains in the complex projective space. An estimate of the Bergman distance is also given.

     

Multiplication operators between Orlicz spaces

The invertible, compact and Fredholm multiplication operators on Orlicz spaces are characterized in this paper.     

Bounded and compact multipliers between Bergman and Hardy spaces

This paper studies the boundedness and compactness of the coefficient multiplier operators between various Bergman spacesA ^p and Hardy spacesH ^q . Some new characterizations of the multipliers between the spaces with exponents 1 or 2 are derived which, in particular, imply a Bergman space analogue of the Paley-Rudin Theorem on sparse sequences. Hardy and Bergman spaces are shown to be linked using mixed-norm spaces, and this linkage is used to improve a known result on (A ^p ,A ²), 1<p<2.Compact (H ¹,H ²) and (A ¹,A ²) multipliers are characterized. The essential norms and spectra of some multiplier operators are computed. It is shown that forp>1 there exist bounded non-compact multiplier operators fromA ^p toA ^q if and only ifpq.     

Multiplication operators on Hilbert spaces of analytic functions

Let be a Hilbert space of functions analytic on a plane domain such that for every in the functional of evaluation at is bounded. Assume further that contains the constants and admits multiplication by the independent variable z, M_z, as a bounded operator. We give sufficient conditions for M_z to be reflexive.Received: 17 February 2004     

Essential norm of differences of weighted composition operators between weighted-type spaces on the unit ball

We find an asymptotically equivalent expression to the essential norm of differences of weighted composition operators between weighted-type spaces of holomorphic functions on the unit ball in C^N. As a consequence we characterize the compactness of these operators. The boundedness of these operators is also characterized.     

Unimodular eigenvalues and invariant measures for linear operators

For a bounded linear operator in a complex separable Hilbert space we show that it accepts an invariant Borel probability measure of square integrable norm whose essential support spans the space, iff its eigenvectors with unimodular eigenvalues span the space.This research has been supported by the Economic Research Center (KOE) of the Athens University of Economics and Business.     

Products of Bergman space Toeplitz operators on the polydisk

Motivated by recent works of Ahern and uković on the disk, we study the generalized zero product problem for Toeplitz operators acting on the Bergman space of the polydisk. First, we extend the results to the polydisk. Next, we study the generalized compact product problem. Our results are new even on the disk. As a consequence on higher dimensional polydisks, we show that the generalized zero and compact product properties are the same for Toeplitz operators in a certain case.The first three authors were partially supported by KOSEF(R01-2003-000-10243-0) and the last author was partially supported by the National Science Foundation.     

Carleson measures for the Drury-Arveson Hardy space and other Besov-Sobolev spaces on complex balls

For 0?σ<1/2 we characterize Carleson measures μ for the analytic Besov-Sobolev spaces on the unit ball Bn in Cn by the discrete tree condition

     

Carleson embeddings and some classes of operators on weighted Bergman spaces

We prove Carleson-type embedding theorems for weighted Bergman spaces with Békollé weights. We use this to study properties of Toeplitz-type operators, integration operators and composition operators acting on such spaces. In particular, we investigate the membership of these operators to Schatten class ideals.     

Dirichlet型空间的Carleson测度和乘子

设0-1,D_α~p表示单位球B_n上满足∫_(B_n)(1-|z|~2)~α|▽f(z)|~pdv(z)<∞的全纯函数全体.对0相似文献   

Bicircular projections on some Banach spaces

In this paper we show that the bicircular projections are precisely the Hermitian projections and prove some immediate consequences of this result.     

A Note on Maximal Inner Spaces of the Bergman Space

For an invariant subspace I of the Bergman space on the unit disk D, the associated inner space I zI has been known to have nice properties K. Zhu has recently given, in terms of kernels of Hankel operators, several characterizations for an inner space to be maximal. We show that maximality of inner spaces can be understood alternatively by use of the adjoint operator of the Bergman shift operator on