Schatten class Toeplitz operators on generalized Fock spaces

Toeplitz Operators on Fock Spaces

Schatten Class Toeplitz Operators on the Bergman Space

Namita Das P. G. Department of Mathematics, Utkal University, Vanivihar, Bhubaneswar, Orissa 751004, India Correspondence should be addressed to Namita Das, [email protected] Received 23 July 2009; Revised 7 September 2009; Accepted 14 October 2009 Recommended by Palle Jorgensen We have shown that if the Toeplitz operator Tφ on the Bergman space La D belongs to the Schatten class Sp, 1 ≤...

Schatten class Toeplitz operators on weighted Bergman spaces of the unit ball

For positive Toeplitz operators on Bergman spaces of the unit ball, we determine exactly when membership in the Schatten classes Sp can be characterized in terms of the Berezin transform.

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 ...

Continuity and Schatten–von Neumann Properties for Pseudo–Differential Operators and Toeplitz operators on Modulation Spaces

Let M (ω) be the modulation space with parameters p, q and weight function ω. We prove that if p1 = p2, q1 = q2, ω1 = ω0ω and ω2 = ω0, and ∂ a/ω0 ∈ L ∞ for all α, then the Ψdo at(x,D) : M p1,q1 (ω1) → M22 (ω2) is continuous. If instead a ∈ M p,q (ω) for appropriate p, q and ω, then we prove that the map here above is continuous, and if in addition pj = qj = 2, then we prove that at(x,D) is a Sc...