Trace class criteria for Toeplitz and composition operators on small Bergman spaces
Peláez, José Ángel · Rättyä, Jouni
Original · EN
We characterize the Schatten class Toeplitz operators induced by a positive Borel measure on the unit disc and the reproducing kernel of the Bergman space A²ω, where ω is a radial weight satisfying the doubling property ∫ᵣ¹ω(s)ds≤ C∫₁₊ᵣ/₂¹ω(s)ds. By using this, we describe the Schatten class composition operators. We also discuss basic properties of composition operators acting from Aᵖω to Aqᵥ.
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