Toeplitz operators on the Dirichlet spaces of planar domains

Fredholm Properties of Toeplitz Operators on Dirichlet Spaces

In this paper, the Fredholm properties of some Toeplitz operators on Dirichlet spaces be discussed, and the essential spectra of Toeplitz operators with symbols in C 1 or H ∞ 1 + C 1 be computed.

Toeplitz Operators on Fock Spaces

Superposition Operators on Dirichlet Spaces

In the context of a strongly local Dirichlet space we show that if a function mapping the real line to itself (and fixing the origin) operates by composition on the left to map the Dirichlet space into itself, then the function is necessarily locally Lipschitz continuous. If, in addition, the Dirichlet space contains unbounded elements, then the function must be globally Lipschitz continuous. T...

Toeplitz Operators on the Bergman Space of Planar Domains with Essentially Radial Symbols

Let Ω be a bounded multiply-connected domain in the complex plane C, whose boundary ∂Ω consists of finitely many simple closed smooth analytic curves γj j 1, 2, . . . , n where γj are positively oriented with respect to Ω and γj ∩ γi ∅ if i / j. We also assume that γ1 is the boundary of the unbounded component of C\Ω. LetΩ1 be the bounded component of C\γ1, and Ωj j 2, . . . , n the unbounded c...

The Commutants of Certain Toeplitz Operators on Weighted Bergman Spaces

For α > −1, let A2α be the corresponding weighted Bergman space of the unit ball in C. For a bounded measurable function f , let Tf be the Toeplitz operator with symbol f on A 2 α. This paper describes all the functions f for which Tf commutes with a given Tg, where g(z) = z1 1 · · · z Ln n for strictly positive integers L1, . . . , Ln, or g(z) = |z1| s1 · · · |zn| nh(|z|) for non-negative real...