TOEPLITZ OPERATORS ON GENERALIZED FOCK SPACES

Toeplitz Operators on Fock Spaces

Toeplitz Operators and Carleson Mea- sures on Generalized Bargmann-Fock Spaces

1.1. Definitions Throughout this paper, λ denotes the Lebesgue measure on C and ωo = dd|z| the Euclidean Kähler form in C, where d = √ −1 4 (∂̄ − ∂). Let φ ∈ C (C) be a function, μ a measure in C, and p ∈ [1,∞). One can define the spaces Lp(e−pφdμ) and F (μ, φ) := Lp(e−pφdμ) ∩ O(C). If the measure μ is Lebesgue measure, we simply write F (λ, φ) =: F (φ). Similarly one can define L∞(e−φ, μ) = {f ...

Products of Toeplitz Operators on the Fock Space

Let f and g be functions, not identically zero, in the Fock space F 2 α of C. We show that the product TfTg of Toeplitz operators on F 2 α is bounded if and only if f(z) = e q(z) and g(z) = ce−q(z), where c is a nonzero constant and q is a linear polynomial.

kTH-ORDER SLANT TOEPLITZ OPERATORS ON THE FOCK SPACE

The notion of slant Toeplitz operators Bφ and kth-order slant Toeplitz operators B φ on the Fock space is introduced and some of its properties are investigated. The Berezin transform of slant Toeplitz operator Bφ is also obtained. In addition, the commutativity of kth-order slant Toeplitz operators with co-analytic and harmonic symbols is discussed.

Finite Rank Toeplitz Operators in Bergman Spaces

We discuss resent developments in the problem of description of finite rank Toeplitz operators in different Bergman spaces and give some applications