TOEPLITZ OPERATORS BETWEEN WEIGHTED BERGMAN SPACES OVER THE HALF-PLANE

In this paper,by characterizing Carleson measures,we investigate a class of bounded Toeplitz operator between weighted Bergman spaces with Békolléweights over the half-plane for all index choices.

TOEPLITZ-TYPE OPERATORS ON LEBESGUE SPACES

Let L be the infinitesimal generator of an analytic semigroup on L 2 (Rn)with Gaussian kernel bounds,and L-α/ 2 be the fractional integrals generated by L for 0< α<n.Let Tj,1 be the singular integral with nonsmooth kernel related to L,or Tj,1=I, Tj,2,Tj,4 be the linear operators,which are bounded on Lp(Rn)for 1<p<∞,and Tj,3=±I(j=1,2,···,m),where I is the identity operator.For b∈L 1 loc (Rn),denote the Toeplitz-type operator byΘαbfmj=1(Tj,1MbIαTj,2 + Tj,3MbIαTj,4),where Mb is a multiplication ope...

TOEPLITZ OPERATORS WITH POSITIVE OPERATOR-VALUED SYMBOLS ON VECTOR-VALUED GENERALIZED FOCK SPACES

In this article,we study some characterizations of Toeplitz operators with positive operator-valued function as symbols on the vector-valued generalized Bargmann-Fock spaces Fψ^2.Main results including Fock-Carleson condition,bounded Toeplitz operators,compact Toeplitz operators,and Toeplitz operators in the Schatten-p class are all considered.

UNBOUNDED COMPLEX SYMMETRIC TOEPLITZ OPERATORS

In this paper,we study unbounded complex symmetric Toeplitz operators on the Hardy space H^(2)(D) and the Fock space g^(2).The technique used to investigate the complex symmetry of unbounded Toeplitz operators is different from that used to investigate the complex symmetry of bounded Toeplitz operators.

TOEPLITZ OPERATORS ASSOCIATED WITH SEMIFINITE VON NEUMANN ALGEBRA

Let H^2（M） be a noncommutative Hardy space associated with semifinite von Neumann algebra M, we get the connection between numerical spectrum and the spectrum of Toeplitz operator Tt acting on H^2（M）, and the norm of Toeplitz operator Tt is equivalent to ｜｜t｜｜ when t is hyponormal operator in M.

COMPLEX SYMMETRY OF TOEPLITZ OPERATORS OVER THE BIDISK

In this paper,we investigate the complex symmetric structure of Toeplitz operators T_(φ)on the Hardy space over the bidisk.We first characterize the weighted composition operators,W_(u,v)which are J-symmetric and unitary.As a consequence,we characterize conjugations of the form A_(u,v).In addition,a class of conjugations of the form C_(λ,a)is introduced.We show that the class of conjugations C_(λ,a)coincides with the class of conjugations A_(u,v);we then characterize the complex symmetry of the Toeplitz operators T_(φ)with respect to the conjugation C_(λ,a).

S_p-CLASS(0

In this paper,we construct a function u in L2,1（Bn,dA）,which is unbounded on any neighborhood of each boundary point of B n,such that Toeplitz operator Tu is compact on Dirichlet space D（Bn,dA）.Furthermore,Schatten p-class（0〈p〈∞） Toeplitz operators on Dirichlet space D（Bn,dA） with unbounded symbols are also obtained.

GALERKIN-PETROV METHODS OF TOEPLITZ OPERATORS ON DIRICHLET SPACE

The convergence of several Galerkin-Petrov methods, including polynomial collocation and analytic element collocation methods of Toeplitz operators on Dirichlet space, is established. In particular, it is shown that such methods converge if the basis and test function own certain circular symmetry.

Toeplitz Operators on the Bergman Space of Multi-connected Domains

In this paper, we investigate the Toeplitz operators with positive measure symbols on the Bergman spaces of bounded multi-connected domains and show that a Toeplitz operator is bounded or compact if and only if the symbol measure is a Carleson or vanishing Carleson measure respectively.

HYPONORMALITY OF BLOCK TOEPLITZ OPERATORS ON THE WEIGHTED BERGMAN SPACES

In this paper we consider the block Toeplitz operators TФ on the weighted Bergman space A2α（D, Cn） and we give a necessary and sufficient condition for the hyponor-mality of block Toeplitz operators with symbol in the class of functions Ф=F ＋ G＊ withmatrix-valued polynomial functions F and G with degree 2.

Commuting Dual Toeplitz Operators on the Polydisk

We completely characterize commutativity of S and Sψ on La2(Dn)⊥ for bounded pluriharmonic symbols and ψ on Dn, and prove that SSψ = Sψ if and only if is analytic or ψˉ is analytic.

SEQUENCES OF POWERS OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE

We consider Toeplitz operators Tu with symbol u on the Bergman space of the unit ball,and then study the convergences and summability for the sequences of powers of Toeplitz operators.We first charactreize analytic symbolsφfor which the sequence Tφ*kf or Tφkf converges to 0 or∞as k→∞in norm for every nonzero Bergman function f.Also,we characterize analytic symbolsφfor which the norm of such a sequence is summable or not summable.We also study the corresponding problems on an infinite direct sum of Bergman spaces as a generalization of our result.

Toeplitz Type Operator Associated to Singular Integral Operator with Variable Kernel on Weighted Morrey Spaces

Suppose T^k,l and T^k,2 are singular integrals with variable kernels and mixed homogeneity or ±I （the identity operator）. Denote the Toeplitz type operator by T^b=k=1∑^QT^k,1M^bT^k,2 where M^bf= bf. In this paper, the boundedness of Tb on weighted Morrey space are obtained when b belongs to the weighted Lipschitz function space and weighted BMO function space, respectively.

TOEPLITZ OPERATORS FROM HARDY SPACES TO WEIGHTED BERGMAN SPACES IN THE UNIT BALL OF C^(n)

We study Toeplitz operators from Hardy spaces to weighted Bergman spaces in the unit ball of C^(n).Toeplitz operators are closely related to many classical mappings,such as composition operators,the Volterra type integration operators and Carleson embeddings.We characterize the boundedness and compactness of Toeplitz operators from Hardy spaces H^(p) to weighted Bergman spaces A_(α)^(q) for the different values of p and q in the unit ball.

Toeplitz Operator Related to Singular Integral with Non-Smooth Kernel on Weighted Morrey Space

Let T1 be a singular integral with non-smooth kernel or ±I, let T2 and T4 be the linear operators and let T3 = ± I. Denote the Toeplitz type operator by Tb = T1M^b Ia T2 ＋ T3IaMbT4,where M^bf = bf, and Ib is the fractional integral operator. In this paper, we investigate the boundedness of the operator Tb on the weighted Morrey space when b belongs to the weighted BMO space.

TOEPLITZ OPERATORS ON HEISENBERG GROUP

Denote by Ω the Siegel domain in Cn, n 〉 1. In this paper, we study the essential spectra of Toeplitz operators defined on the Hardy space H2（а↓Ω）. In addition, the characteristic equation of analytic Toeplitz operators iааs obtained.

Reducing Subspaces of Toeplitz Operators on N_φ-type Quotient Modules on the Torus

In this paper, we prove that the Toeplitz operator with finite Blaschke product symbol Sψ（z） on Nφ has at least m non-trivial minimal reducing subspaces, where m is the dimension of H^2（Гω）⊙φ（ω）H^2（Гω）. Moreover, the restriction of Sψ（z） on any of these minimal reducing subspaces is unitary equivalent to the Bergman shift Mz.

Commuting Toeplitz Operators with Harmonic Symbols on A^2(■,dμ)

For any given symmetric measure μ on the closed unit disk D, we apply the Berezin transform to characterizing semi-commuting and commuting Toeplitz operators with bounded harmonic symbols on A2（D, dμ）.

COMPACT TOEPLITZ OPERATORS ON A^P (φ)(1

Let φ be a normal function defined on [0, 1) and A^p(φ) Bergman space weighted with φ~p(|z|)/(1-|z|~2) for 1≤p<∞. The compactnesses of Toeplitz operaters on A^p(φ) are characterized by Carleson measures and operator algebra.

к-order Slant Toeplitz Operators on the Bergman Space

In this paper k-order slant Toeplitz operator on the Bergman space is defined. Some properties like spectrum, commuting are discussed.